A possible tension between galaxy rotational velocity and observed physical properties

Lior Shamir and Darius McAdam
Kansas State University
Manhattan, KS 66506

Abstract

The discrepancy between the mass of galaxies and their rotational velocity is one of the most puzzling scientific phenomena. Despite over a century of research, this phenomenon is not fully understood. Common explanations include dark matter and MOND, among other theories. Here we report on another observation that shows tension between the physics of galaxy rotation and its rotational velocity. We compare the brightness of galaxies, and find that galaxies that spin in the same direction as the Milky Way have different brightness than galaxies that spin in the opposite direction. While such difference in brightness is expected due to Doppler shift, it is expected to be subtle. The results show that the difference in brightness is large enough to be detected by Earth-based telescopes. That observed difference corresponds to physical properties of galaxies with far greater rotational velocity than the rotational velocity of the Milky Way. The brightness difference is consistent in both the Northern galactic pole and the Southern galactic pole, and is not observed in parts of the sky that are perpendicular to the galactic pole. The differences are observed by several different instruments such DECam, SDSS, Pan-STARRS, and HST. The observation is also consistent across annotation methods, including different computer-based methods, manual annotation, or crowdsourcing annotations through “Galaxy Zoo”, all show similar results. Another possible explanation to the observation is parity violation in the large-scale structure, such that the magnitude of the parity violation was stronger in the earlier Universe. It can also be linked to other anomalies such as the $H_{o}$ tension. Analysis of $H_{o}$ using Ia supernovae shows smaller $H_{o}$ tension when the spin directions of the host galaxies are consistent, although these results are based on a small number of supernovae, and may not be statistically significant.

Keywords: Galaxy: general, galaxies: spiral, Cosmology: large-scale structure of universe, Cosmology: Cosmic anisotropy

1 Introduction

Despite over a century of research, the galaxy rotation curve anomaly (Opik,, 1922; Babcock,, 1939; Oort,, 1940; Rubin and Ford Jr,, 1970; Rubin et al.,, 1978, 1980, 1985; Sofue and Rubin,, 2001) is still an unexplained observation. Early evidence that the galaxy rotation disagree with the physical properties of galaxies were observed as early as the first half of the 20th century (Slipher,, 1914; Wolf,, 1914; Pease,, 1918; Babcock,, 1939; Mayall,, 1951). In fact, the absence of Keplerian velocity decrease in the outer parts of galaxies was observed shortly after it became clear that galaxies are rotating objects (Rubin,, 2000).

For instance, one of the most detailed early observations of the galaxy rotation curve anomaly was made by Jan Hendrik Oort, who analyzed the rotation and mass distribution of NGC 3115 (Oort,, 1940). That work led to the conclusion that “the distribution of mass in the system appears to bear almost no relation to that of light”, and that “the strongly condensed luminous system appears embedded in a large and more or less homogeneous mass of great density”.

While that early work identified what is now considered the dark matter halo, preeminent astronomers of the time argued that the galaxy rotation was driven by Newtonian dynamics corresponding to the distribution of the visible light (De Vaucouleurs,, 1959; Schwarzschild,, 1954), which was based on the theory of that time. According to Rubin, (2000), these opinions played a substantial role in ignoring the observations of the galaxy rotation curve anomaly, and led to adopting an incorrect Newtonian model as the physical model of galaxy rotation. Only several decades later the observations that galaxy rotation does not follow any known physical model was accepted by the “mainstream” astronomy community (Rubin,, 2000).

After the tension between the galaxy rotation and its physical properties became an accepted observation, theoretical explanations were proposed. Perhaps the most common explanation to the anomaly is that the mass of the galaxy is dominated by dark matter (Zwicky,, 1937) that does not interact with light or with any other known form of radiation (Rubin,, 1983). While this explanation is widely accepted, there is still no direct conclusive evidence for the existence of dark matter (Sanders,, 1990; Mannheim,, 2006; Kroupa,, 2012; Kroupa et al.,, 2012; Kroupa,, 2015; Arun et al.,, 2017; Bertone and Tait,, 2018; Skordis and Złośnik,, 2019; Sivaram et al.,, 2020; Hofmeister and Criss,, 2020), and research efforts are still being continued. The dominance of the dark matter halo in spiral galaxies was also challenged by the properties of their rotation curves (Byrd and Howard,, 2019, 2021). The initial contention that the distribution of dark matter in the galaxy is constant (Oort,, 1940; Donato et al.,, 2009) is in certain disagreement with its correlation with light and other galactic disk properties (Zhou et al.,, 2020). Research efforts towards understanding the existence and nature of the contention that the mass of galaxies is dominated by dark matter are still being continued.

Another common paradigm related to the galaxy rotation curve anomaly is that galaxy rotation can be explained by modifications of the Newtonian Dynamics (Milgrom,, 1983, 2007; De Blok and McGaugh,, 1998; Sanders,, 1998; Sanders and McGaugh,, 2002; Swaters et al.,, 2010; Sanders,, 2012; Iocco et al.,, 2015; Díaz-Saldaña et al.,, 2018; Falcon,, 2021). While dark matter became pivotal in standard cosmological models, the Modified Newtonian Dynamics (MOND) also showed agreement with observations (Kroupa,, 2015; O’Brien et al.,, 2017; Wojnar et al.,, 2018; Milgrom,, 2019), although other studies have shown tension between MOND predictions and data (Dodelson,, 2011; Zhou et al.,, 2020). Other explanations have also been proposed, such as (Sanders,, 1990; Capozziello and De Laurentis,, 2012; Chadwick et al.,, 2013; Farnes,, 2018; Rivera,, 2020; Nagao,, 2020; Blake,, 2021; Larin,, 2022). But despite over a century of research, the physical nature of galaxy rotation is still a mystery, with no single proven and complete physical explanation.

1.1 Previous reports on possible asymmetry in the distribution of galaxy spin directions

While this study does not focus on the large-scale structure of the Universe, the observation reported here can be linked to certain observed anomalies in the large-scale structure reported in previous studies. One of these observations is the $H_{o}$ tension, as will be discussed in Section 8. Another observation is the proposed anomaly of asymmetry between the number spiral galaxies that spin in opposite directions, as observed from Earth. If the asymmetry reflects the large-scale structure of the Universe it might conflict with the standard cosmological theories. The results of this study propose that the observation is not necessary related to the large-scale structure, but to internal structure of galaxies. The relevance of the distribution of galaxy spin directions as observed from Earth to this study will be explained in Section 1.3. The direct explanation of the observation described in this paper and the possible observed yet unexpected asymmetry between the number of galaxies spinning in opposite directions will also be discussed in detail in Section 1.3.

The observation that the number of galaxies spinning towards one direction is not necessarily the same as the number of galaxies spinning in an opposite direction was noted as early as the mid 1980’s, although with a relatively small number of galaxies (MacGillivray and Dodd,, 1985). The deployment of autonomous digital sky surveys allowed research with a much larger number of galaxies. Some experiments were based on manual annotations of the galaxies carried out by undergraduate students (Longo,, 2011), and other studies used automatic analysis of a large number of galaxies, as many as $\sim 10^{6}$ galaxies (Shamir, 2022a, ) or more (Shamir, 2022b, ) in a single experiment. The findings are consistent across different telescopes such as SDSS (Longo,, 2011; Shamir,, 2012; Shamir, 2019b, ; Shamir, 2020c, ; Shamir, 2022e, ), Pan-STARRS (Shamir, 2020c, ), HST (Shamir, 2020b, ), DECam (Shamir, 2021b, ), DES (Shamir, 2022c, ; Shamir, 2022d, ), and the DESI Legacy Survey (Shamir, 2022b, ). Smaller scale studies showed correlation in spin directions (Lee et al., 2018b, ; Lee et al., 2018a, ), also when the galaxies are too far from each other to have gravitational interactions (Lee et al., 2019a, ; Lee et al., 2019b, ), an observation that was defined as “mysterious” (Lee et al., 2019b, ).

According to that previous work, all telescopes and all analysis methods show a dipole axis exhibited by the spin directions of spiral galaxies (Shamir, 2022c, ; Shamir, 2022d, ; Shamir, 2022b, ). That is, according to these reports the sky can be separated into two hemispheres, such that one hemisphere has a higher number of galaxies spinning clockwise, and the opposite hemisphere has a higher number of galaxies spinning counterclockwise. When using a large number of galaxies, a shifted window with $90^{o}$ radius can be used to deduce the asymmetry in all possible hemispheres (Shamir, 2022b, ). Panel (g) in Figure 1 shows the results of the asymmetry between the number of clockwise and counterclockwise galaxies in the hemisphere centered at each point in the sky, computed from a set of $\sim 1.3$ million galaxies imaged by the DESI Legacy Survey. That experiment is described in detail in (Shamir, 2022b, ), and its results show the asymmetry between hemispheres without an attempt to fit the spin directions into a certain statistical model. Fitting the spin directions into cosine dependence is shown in Panels (a) through (f), and suggest a statistically significant fitness into a dipole axis (Shamir, 2020c, ; Shamir, 2020b, ; Shamir, 2021b, ; Shamir, 2022a, ; Shamir, 2022c, ).

Refer to caption — Figure 1: Results of the analysis of dipole axes observed in different telescopes. The graphs show the probability to have a dipole axis by mere chance from each point in the sky. The analyses are taken from previous experiments (Shamir, 2020c, ; Shamir, 2020b, ; Shamir, 2021b, ; Shamir, 2022a, ; Shamir, 2022c, ; Shamir, 2022b, ). The analyses shown in Panels (a) through (f) are based on statistical fitness of the distribution of spin directions into a dipole axis (Shamir, 2020c, ; Shamir, 2020b, ; Shamir, 2021b, ; Shamir, 2022a, ; Shamir, 2022c, ). The analysis shown in panel (g) is based on direct measurements of the difference in spin direction around each point in the sky.

On the other hand, several studies suggested that the spin directions are random. These studies are discussed in (Shamir, 2022f, ) as well as (Shamir, 2022b, ; Shamir, 2022a, ; Shamir, 2022c, ). In summary, Iye and Sugai, (1991) used $\sim 6.5\cdot 10^{3}$ galaxies and found no statistically significant non-random signal. As explained in (Shamir, 2022f, ), the dataset was too small to show statistical significance, as showing a $2\sigma$ statistical significance in that manner requires at least $2.7\cdot 10^{4}$ galaxies.

Land et al., (2008) used SDSS galaxies annotated by anonymous volunteers, and showed a much higher number of galaxies spinning counterclockwise, which was the result of human bias in the annotation. After mirroring a small subset of these galaxies to correct for the human bias, the data showed 1.5%-2% more galaxies spinning counterclockwise. The small number of galaxies did not allow statistical significance (P $\simeq$ 0.13), but the direction and magnitude of that asymmetry is fully consistent with automatic analysis of SDSS galaxies in the same footprint (Shamir, 2020c, ).

An analysis of SDSS galaxies from the same footprint was done by applying automatic annotation using the SpArcFiRe algorithm (Davis and Hayes,, 2014), and included a much higher number of galaxies (Hayes et al.,, 2017). When applied to galaxies annotated as spirals by Galaxy Zoo 1, the asymmetry was statistically significant. Applying a machine-learning algorithm to annotate the galaxies showed random distribution, but that was observed after removing specifically all attributes that correlated with the asymmetry in galaxy spin directions. The removal of the attributes that correlate with the asymmetry naturally led to a symmetric dataset, as demonstrated experimentally in (Shamir, 2022f, ).

Repeating the experiment of (Hayes et al.,, 2017) by applying the same SpArcFiRe algorithm¹¹1https://github.com/waynebhayes/SpArcFiRe to 666,416 SDSS galaxies used in Galaxy Zoo 1 without applying any form of pre-selection led to a dataset of 273,166 annotated galaxies. Figure 2 displays the statistical strength of a dipole axis in the galaxy spin directions in all parts of the sky. The Figure shows a dipole axis peaking at around $(\alpha=171^{o},\delta=37^{o})$ , with statistical strength of 6.95 $\sigma$ . This experiment might not provide a complete proof to the existence of a dipole axis in galaxy spin directions, but it also does not conflict with previous experiments such as the results shown in Figure 1.

An interesting argument that the distribution of spin directions is random was made by Iye et al., (2021), who proposed that the observed asymmetry is the result of duplicate objects in the dataset used in (Shamir, 2017c, ). However, no argument for the existence of any form of axis was made in (Shamir, 2017c, ), and no argument for any kind of axis in that dataset was made in any other paper. More importantly, a simple analysis of that same “clean” dataset shows that it is not at all random (Shamir, 2022f, ). For instance, Table 1 shows a very simple analysis of separating the exact same dataset used by Iye et al., (2021) into two opposite hemispheres, showing that the distribution of spin directions form two hemispheres with inverse asymmetry (Shamir, 2022f, ). Even if assuming that the distribution in the less populated hemisphere is random, a Bonferroni correction shows probability of $\sim 0.01$ . A Monte Carlo simulation shows probability of $\sim 0.007$ . Code and data to reproduce the analysis is available in https://people.cs.ksu.edu/~lshamir/data/iye_et_al.

Hemisphere	# cw	# ccw	$\frac{\#Z}{\#S}$	P
(RA)				(one-tailed)
$70^{o}-250^{o}$	23,037	22,442	1.0265	0.0026
$>250^{o}\cup<70^{o}$	13,660	13,749	0.9935	0.29

Table 1: The distribution of spin directions in the “clean” dataset used in (Iye et al.,, 2021).

Analysis of a dipole axis in that dataset using Equation 2 in (Iye et al.,, 2021) shows a dipole axis with statistical significance of 2.14 $\sigma$ (Shamir, 2022b, ). That analysis is shown in Panel (d) of Figure 1. The exact same data used in (Iye et al.,, 2021), the code that implements the analysis, step-by-step instructions for reproducing the analysis, and the output of the analysis are available in https://people.cs.ksu.edu/~lshamir/data/iye_et_al. More information is provided in (Shamir, 2022f, ; Shamir, 2022b, ; Shamir, 2022a, ; Shamir, 2022c, ).

1.2 Difference in brightness between galaxies spinning in opposite directions

A related observation is that galaxies that spin clockwise have, on average, different brightness than galaxies spinning counterclockwise. That is, in one hemisphere galaxies that spin clockwise are slightly brighter than counterclockwise galaxies, while in the opposite hemisphere galaxies that spin counterclockwise are brighter.

Unlike the asymmetry between the number of galaxies spinning clockwise and the number of galaxies spinning counterclockwise, the difference in brightness of galaxies is a relatively new research question. The first report on the differences in colors between galaxies based on their spin direction was based on SDSS galaxies, with mild statistical significance (Shamir,, 2013). That simple experiment included galaxies from SDSS with no separation to hemispheres or different parts of the sky. Further analysis showed differences in a large number of photometric measurements, but due to the large number of measurements tested no statistical significance was observed after applying a Bonferroni correction (Hoehn and Shamir,, 2014).

Another experiment showed that by separating SDSS galaxies by their spin direction, a machine learning algorithm was able to predict the spin directions of the galaxies by their photometric attributes in accuracy far greater than mere chance (Shamir,, 2016). That provided an indication that extra-galactic objects that spin in opposite directions are also photometrically different from each other. The dataset used in the experiment was too small to show statistically significant differences of specific measurements, but it provided early evidence of difference between the brightness of galaxies that spin clockwise, compared to the brightness of galaxies that spin counterclockwise.

Separating into two hemispheres showed that in one hemispheres objects identified by the photometric pipeline as extended objects that spin clockwise are brighter, while in the opposite hemisphere objects that spin counterclockwise are brighter (Shamir, 2017b, ). Similarly, color differences were also noted (Shamir, 2017a, ). The asymmetry was observed to peak very close to the galactic pole (Shamir, 2017b, ). A similar observation was also made with a smaller number of HST galaxies (Shamir, 2020a, ). The proximity of the peak of the asymmetry in galaxy brightness to the galactic pole led to the contention that the difference in brightness might be related to the rotational velocity of galaxies, and differences between galaxies that spin with the Milky Way compared to the brightness of galaxies that spin in the opposite direction (Shamir, 2017b, ; Shamir, 2020a, ). The difference was noticed not just from the data in the photometric pipelines of the sky surveys, but also in the analysis of the images (Shamir, 2022g, ). Explanations included anomalies in the large-scale structure, or in the internal structure of galaxies (Shamir, 2020a, ).

1.3 A possible link between brightness difference and the observed population of spiral galaxies with opposite spin directions

Since every telescope has a limiting magnitude, the number of galaxies observed by that telescope is a direct function of the apparent brightness of the objects. Therefore, if in one hemisphere galaxies that spin clockwise are brighter than galaxies that spin counterclockwise, more galaxies spinning clockwise will be imaged, leading to a higher number of clockwise galaxies observed in that hemisphere. Similarly, brighter counterclockwise galaxies in the opposite hemisphere will lead to a higher number of galaxies spinning counterclockwise observed in that hemisphere. Therefore, an assumption that the brightness of a galaxy depends on its spin direction relative to the Milky Way can lead directly to an observed difference in the number of galaxies spinning in opposite directions.

Assuming that the brightness of a galaxy is related to its spin direction relative to the Milky Way, the difference between the number of clockwise and counterclockwise galaxies is expected to peak at around the galactic pole. The opposite side of the galactic pole is expected to show inverse asymmetry between galaxies with opposite spin directions, and that difference is expected to exhibit itself in the form of cosine dependence in other parts of the sky. As discussed in Section 1.1, the asymmetry between the number of clockwise and counterclockwise galaxies can be fitted to cosine dependence with strong statistical significance, and form a dipole axis. Table 2 shows the most likely dipole axes determined in several different previous studies using several different telescopes.

Paper	Telescope	RA	Dec
reference		(degrees)	(degrees)
(Shamir, 2020c, )	SDSS	229	-21
(Shamir, 2020c, )	Pan-STARRS	227	1
(Longo,, 2011)	SDSS	217	32
(Shamir,, 2016)	SDSS	165	30
(Shamir, 2021a, )	SDSS	165	40
(Land et al.,, 2008)	SDSS	161	11
(Shamir,, 2012)	SDSS	132	32
(Shamir, 2022b, )	DESI	243	39
(Shamir, 2021b, )	DECam	237	10
(Shamir, 2022c, )	DES	255	47
(Shamir, 2022a, )	Combined	229	19

Table 2: The most likely dipole axis in the large-scale distribution of galaxy spin direction as reported in several different previous studies.

As the table shows, the location of the most likely dipole axes are in close proximity to the galactic pole at $(\alpha=192^{o},\delta=27^{o})$ . That is shown visually in Figure 3. The locations of these axes are determined statistically, and therefore have certain statistical error. They are not aligned perfectly with the galactic pole, and the agreement can also be a coincidence. But the locations of these axes and their proximity to the galactic pole also do not conflict with the contention of a possible link between the galactic pole and the observation briefly mentioned in Section 1.1, and will be discussed in much more details in the rest of this paper.

1.4 Relativistic beaming and the link between galaxy brightness and its spin direction

Relativistic beaming has been studied in the context of high-velocity phenomena such as radio jets (Cohen et al.,, 2007; Savolainen et al.,, 2010), but was also analyzed statistically with quasars and radio galaxies (Orr and Browne,, 1982; Ishwara-Chandra and Saikia,, 2000), and a correlation has been reported between the flux and motion (Wills and Browne,, 1986). Interestingly, while it was found that relativistic beaming determines the observed flux in radio quasars (Padovani and Urry,, 1992), the observed statistical properties do not agree with the expected physical effect of relativistic beaming alone (Heinz and Merloni,, 2004; Odo et al.,, 2017). It has been suggested that relativistic beaming can lead to radio source asymmetry (Alhassan et al.,, 2019).

In addition to radio sources, relativistic beaming has been related to the light curve of active galactic nuclei (Lister,, 2001), black hole emission ring (Rummel and Burgess,, 2020), and binary black holes (Hayasaki and Loeb,, 2016). It has also been proposed that relativistic beaming can lead to certain statistical asymmetry when observing a population of galaxies (Alam et al.,, 2017).

According to relativistic beaming, a galaxy that rotates in the same direction as the Milky Way is expected to be have different brightness to an Earth-based observer compared to an identical galaxy that spins in the opposite direction. The brightness of a galaxy the brightness of its stars and other luminous objects, most of them are in a spin motion around the galaxy center. A star or any other light-emitting object in a spiral galaxy rotating at velocity $V_{r}$ relative to a stationary observer will have a Doppler shift of its bolometric flux F. The expected observed flux F of a galaxy can be calculated by Equation 1

F=F_{o}(1+4\cdot\frac{V_{r}}{c}),

(1)

where $F_{o}$ is the flux of the luminous object if it was stationary relative to the observer, and $c$ is the speed of light (Loeb and Gaudi,, 2003; Rybicki and Lightman,, 2008). Assuming that $\frac{v}{c}$ is $\sim$ 0.0007 as is approximately the case of the Sun in the Milky Way, a star rotating in the opposite direction compared to the Milky Way and observed on the galactic pole of the Milky Way will have $\frac{v}{c}$ of 0.0014 relative to an Earth-based observer. The $\frac{F}{F_{0}}$ of that star as observed from the Solar system is therefore $\simeq$ 1.0056. The brightness of a galaxy is driven by the total brightness of its luminous objects, and therefore the maximal expected difference between the magnitude of a face-on galaxy on the galactic pole that rotates in the same direction as the Milky Way and the magnitude of an identical galaxy spinning in the opposite way is $-2.5\log_{10}1.0056\simeq 0.006$ .

When the galaxy spins, its $F_{o}$ cannot be measured directly, and therefore $\frac{F}{F_{o}}$ cannot be determined observationally for a single galaxy. But when observing a large population of galaxies in the field around the galactic pole, the mean magnitude of the galaxies spinning in the same direction of the Milky Way can be compared to the mean magnitude of galaxies spinning in the opposite direction of the Milky Way. When a large number of galaxies is used, a statistically significant difference between the galaxy magnitude is expected. The purpose of this study is to compare the brightness of face-on galaxies spinning in the same direction as the Milky Way, and galaxies that spin in the opposite direction. That galaxies are imaged by the Dark Energy Camera (DECam) and other instruments at around the galactic pole.

The practice of using a large number of galaxies when a measurement is not possible with a single galaxy is a practice used in other tasks such as weak lensing (Van Waerbeke et al.,, 2000; Wittman et al.,, 2000; Mandelbaum et al.,, 2006; Hirata et al.,, 2007). Here, the expected difference of 0.006 magnitude cannot be measured for a single galaxy, and therefore is measured as the mean magnitude of a large number of galaxies. To observe the maximum difference of 0.006 magnitudes, all galaxies need to be pure face-on galaxies, with no inclination, and all of them are expected to be exactly on the galactic pole of the Milky Way. These conditions are not practical, and therefore the expected observed difference is expected to be of less then 0.006 magnitudes.

2 DECam Data

The Dark Energy Camera (DECam) is placed on the Víctor M. Blanco 4m telescope in Cerro Tololo (Flaugher et al.,, 2012). Its footprint covers both the Northern and Southern galactic pole, allowing to compare them using the same instrument. The DECam data used in this study includes the two $60^{o}\times 60^{o}$ fields centered around the Northern and Southern galactic pole. Additionally, two fields at $90^{o}$ from the galactic pole were used as control fields. The images were retrieved from the DESI Legacy Survey Dey et al., (2019) server using the Cutout API. The images that were retrieved were images of objects identified as galaxies by the DESI Legacy Survey DR8 pipeline, and had magnitude lower than 19.5 in the g, r, or z band. Each image is a 256 $\times$ 256 JPEG image, and the images were scaled using the Petrosian radius to ensure that the galaxy fits in the image. Because the objects are identified by the DESI Legacy Survey pipeline as extended objects, in some cases multiple objects can be part of the same galaxy. To ensure that each galaxy is represented once in the dataset, objects that have another object in the dataset within 0.01^o are excluded from the dataset. The fields and the number of galaxies imaged by DECam in each field are specified in Table 3.

Table 3: The

(\alpha,\delta)

coordinates of the centered and the number of galaxies in each

60^{o}\times 60^{o}

field.

Field	# galaxies
center
$(192^{o},27^{o})$	1,309,498
$(12^{o},-27^{o})$	6,376,803
$(102^{o},0^{o})$	1,377,789
$(282^{o},0^{o})$	1,266,036

The galaxies were separated by their spin directions using the Ganalyzer algorithm Shamir, (2011) as described in Shamir, (2016); Shamir, 2017b ; Shamir, 2020c ; Shamir, 2017c ; Shamir, 2021b . Ganalyzer is a deterministic model-driven algorithm that follows defined symmetric rules. It is not based on machine learning or complex data-driven rules that lead to non-intuitive classification schemes, and therefore its symmetric nature can be defined. The symmetricity of the algorithm ensures that the algorithm is not systematically biased, which is far more difficult to verify when using algorithms based on complex non-intuitive rules as typical in approaches such as deep neural networks.

In summary, the algorithm works by first converting each galaxy image into its radial intensity plot. The radial intensity plot of a galaxy image is a 35 $\times$ 360 image, in which the pixel $(x,y)$ is the median value of the 5 $\times$ 5 pixels around pixel coordinates $(O_{x}+\sin(\theta)\cdot r,O_{y}-\cos(\theta)\cdot r)$ in the original image, where r is the radial distance in percentage of the galaxy radius, $(O_{x},O_{y})$ is the center of the galaxy, and $\theta$ is the polar angle measured in degrees from the galaxy center.

Pixels on the arm of the galaxy are expected to be brighter than pixels at the same radial distance that are not on the arm, and therefore peaks in the radial intensity plot are expected to correspond to pixels on the arms of the galaxy. The arms can therefore be identified by applying a peak detection algorithm (Morháč et al.,, 2000) to the different lines in the radial intensity plot. After the peaks are identified, a linear regression is applied to the peaks in neighboring lines. The sign of the slope of the lines formed by the peaks reflects the direction of the curves of the arms, and consequently the spin direction of the galaxy Shamir, (2016); Shamir, 2017b ; Shamir, 2020c ; Shamir, 2017c ; Shamir, 2021b . Figure 4 shows an example of galaxy images, the radial intensity plots rendered from each galaxy image, and the peaks identified in the radial intensity plots.

Many galaxies are elliptical, and their spin directions cannot be determined. Other galaxies might not be elliptical, but still do not have identifiable direction of their spin. To reject galaxies that their spin direction cannot be determined, only galaxies that have three times more peeks in one direction compared to the other direction, and at least 30 identified peaks in their radial intensity plot Shamir, (2016); Shamir, 2017b ; Shamir, 2017c ; Shamir, 2020c ; Shamir, 2021a ; Shamir, 2021b . The full description of the Ganalyzer algorithm is available in Shamir, (2011); Dojcsak and Shamir, (2014); Shamir, (2016); Shamir, 2017b ; Shamir, 2017c ; Shamir, 2020c ; Shamir, 2021b .

The simple “mechanical” nature of Ganalyzer ensures that it is symmetric, as was also tested empirically in several previous studies. For instance, Figure 5 and Figure 9 in (Shamir, 2022c, ) show the results of the annotation after mirroring the galaxy images. A certain downside of using such analysis is that the annotation is not complete in the sense that all galaxies that have a spin direction are indeed annotated. Figure 5 shows an example of galaxies imaged by DECam, and the same galaxies imaged by Hubble Space Telescope (HST). As the figure shows, galaxies that have clear spin direction would be annotated as galaxies that do not have an identifiable spin direction, and therefore rejected from the analysis. Clearly, using HST images will also be subjected to incompleteness, as HST has its own limits on its imaging power. Since no telescope can provide a complete dataset in which the spin directions of all galaxies can be identified, the importance of the algorithm is its symmetric nature.

After separating the galaxy images by their spin directions, 400 random galaxies were observed, and none of these galaxies had a spin direction opposite to the spin direction it was annotated by the algorithm. While that does not ensure that the entire dataset does not have any wrongly annotated galaxies, it can be safely assumed that the dataset was into two subsets such that one subset has a much higher frequency of galaxies that spin clockwise, and the other subset has a much higher frequency of galaxies spinning counterclockwise. Another subset includes galaxies that their spin direction could not be determined, but due to the symmetric nature of the algorithm that subset is not expected to affect the ratio between the other two subsets. As will be shown in Section 3, the inverse results in the opposite sides of the Galactic pole show no consistent bias of the algorithm.

3 Results of DECam data

Tables 4 and 5 show the difference between the mean magnitude of galaxies spinning in opposite ways in the fields around the North and the South galactic pole, respectively. To avoid potential erroneous magnitude values that can skew the mean magnitude, all magnitude values lower than 10 or greater than 25 were rejected from the analysis. The bands that were used in this study are the three optical bands of DESI Legacy Survey, which are the g, r, and z bands. Some galaxies do not have values for the flux in all bands, and that leads to a slightly different number of galaxies used in each band.

The tables show the differences in the mean brightness between galaxies that spin in opposite directions at the field around the galactic poles. The tables show that the differences are statistically significant, as determined by the one-tailed P values of the Student t-test (Helmert,, 1876). While the differences in magnitude are observed in both hemispheres, the direction of the difference is inverse, such that clockwise galaxies are brighter in one hemisphere but dimmer i the opposite hemisphere.

The inverse difference in magnitude agrees with the expected difference caused by relativistic beaming in the two opposite sides of the galactic pole. It also shows that it is not caused by a bias of the annotation algorithm of photometric pipeline, as such bias is expected to be consistent across different fields, and is not expected to flip between the North and South galactic poles.

Table 4: The g, r, and z magnitude and the number of clockwise and counterclockwise galaxies in the

60^{o}\times 60^{o}

field centered around the North galactic pole

(\alpha=192^{o},\delta=27^{o})

Band	# cw	# ccw	Mag	Mag	$\Delta Mag$	t-test P
	galaxies	galaxies	ccw	cw
G	20,918	21,253	20.06525 $\pm$ 0.010	20.10073 $\pm$ 0.010	-0.03548	0.01
R	20,917	21,251	18.98522 $\pm$ 0.008	19.01481 $\pm$ 0.008	-0.02958	0.01
Z	20,925	21,261	18.2934 $\pm$ 0.007	18.31783 $\pm$ 0.007	-0.02443	0.01

Table 5: The magnitude and number of clockwise and counterclockwise galaxies in the field centered around the South galactic pole

(\alpha=12^{o},\delta=-27^{o})

Band	# cw	# ccw	Mean	Mean	$\Delta Mag$	t-test P
	galaxies	galaxies	Mag ccw	Mag cw
G	87,640	89,534	20.13622 $\pm$ 0.004	20.11937 $\pm$ 0.004	0.01685	0.003
R	87,917	89,849	19.08793 $\pm$ 0.003	19.07216 $\pm$ 0.003	0.01574	0.0002
Z	88,228	90,142	18.38424 $\pm$ 0.003	18.37225 $\pm$ 0.003	0.01199	0.0047

Although the difference in magnitude around the galactic pole can be expected, in all cases the observed magnitude differences in both the Northern and Southern galactic poles are larger than the maximum expected difference in optimal conditions. As discussed in Section 1.4, the maximum expected magnitude difference expected under optimal conditions between galaxies at the galactic pole spinning in opposite ways is $\sim$ 0.006. For instance, the difference in the G band around the Northern galactic pole is $\sim$ 0.03548, which is larger than the expected maximum difference of 0.006. Because the standard error of the magnitude difference is $\sim$ 0.0142, the observed difference is larger by $\sim 2.1\sigma$ from the expected magnitude difference. From the six measurements in Tables 4 and 5, the only measurement that does not meet the 0.05 P-value threshold for the difference between the expected and observed magnitude difference is the Z band of the Southern pole, with P $\simeq$ 0.08. Clearly, all measurements show strong statistical significance when assuming that the brightness of clockwise and counterclockwise galaxies around the galactic pole is the same. Because the galaxies in the Northern galactic pole are different galaxies than the galaxies in the South galactic pole, the two tests can be considered independent, and therefore the P value of the two tests is P $<0.0357\cdot 0.08$ , and therefore $P<0.0028$ .

Tables 4 and 5 also show a difference between the number of galaxies that spin clockwise and the number of galaxies that spin counterclockwise. That difference agrees with the magnitude difference, as it is expected that if one type of galaxies is brighter to an Earth-based observer than the other type, more galaxies of that type will be identified. The previous reports on the large-scale differences between the number of galaxies spinning in opposite directions are specified in Section 1.1, and their link to brightness differences is discussed in Section 1.3. In summary, if one type of galaxies is indeed brighter to an Earth-based observer, the observed difference in the number of galaxies spinning in opposite directions can be the result of the difference in magnitude rather than the real population of spiral galaxies in the Universe.

The difference between the mean magnitude of galaxies spinning in opposite directions around the fields of the Northern and Southern galactic poles was compared to the two control fields that were selected as fields that are 90^o away from the galactic pole. Tables 6 and 7 show the difference in magnitude around these fields. The tables use 47,017 and 41,244 galaxies, respectively. As both tables show, there is no statistically significant magnitude difference between the galaxies in these two fields. That shows that in 90^o from the galactic pole, there is no observed difference between the brightness of galaxies spinning in opposite ways, as is the case for galaxies at around the galactic pole. That can be viewed as a link between the galactic pole and the differences in the brightness of galaxies spinning in opposite directions.

Table 6: The mean magnitude of clockwise and counterclockwise galaxies in the

60^{o}\times 60^{o}

window centered around the control field of

(\alpha=102^{o},\delta=0^{o})

Band	Mag	Mag	$\Delta Mag$	P
	ccw	cw
G	20.16695 $\pm$ 0.009	20.16628 $\pm$ 0.009	0.000669	0.96
R	19.09924 $\pm$ 0.007	19.10284 $\pm$ 0.007	-0.00356	0.713
Z	18.39402 $\pm$ 0.006	18.39436 $\pm$ 0.006	-0.00032	0.972

Table 7: The mean magnitude of clockwise and counterclockwise galaxies in the

60^{o}\times 60^{o}

window centered around the control field of

(\alpha=282^{o},\delta=0^{o})

Band	Mag	Mag	$\Delta Mag$	P
	ccw	cw
G	20.21329 $\pm$ 0.01	20.22103 $\pm$ 0.01	-0.00774	$0.58$
R	19.0787 $\pm$ 0.008	19.0869 $\pm$ 0.008	-0.0082	0.47
Z	18.37519 $\pm$ 0.007	18.37565 $\pm$ 0.007	-0.00045	0.96

4 Experiment with SDSS galaxies

DECam provides images of a large number of galaxies, but until the Dark Energy Spectroscopic Instrument (DESI) sees first light most of these galaxies do not have spectra. To test a set of galaxies with spectra we used SDSS data. SDSS is inferior to DECam in its imaging capabilities, but as a mature redshift survey it collected spectra for a relatively high number of galaxies.

Images of 666,416 galaxies were downloaded by using the SDSS cutout API. The initial file format was 128 $\times$ 128 JPEG, and each file was converted to the PNG format. These images were annotated by the SpArcFiRe (Scalable Automated Detection of Spiral Galaxy Arm) algorithm (Davis and Hayes,, 2014; Hayes et al.,, 2017). To test for consistency, the galaxy images were also mirrored by using the “flip” command of ImageMagick. That led to two annotated datasets, the first is the annotations of the original images, and the other is the annotations of the mirrored images. SpArcFiRe is an open source software with available source code²²2https://github.com/waynebhayes/SpArcFiRe. SpArcFiRe is described in detail in (Davis and Hayes,, 2014). The method works by identifying arm segments, and can then fit these segments to a logarithmic spiral arc. That allows SpArcFiRe to determine the spin direction of the galaxy. SpArcFiRe is a model-driven method, and is not based on machine learning that can lead to biases that are vgery difficult to detect (Dhar and Shamir,, 2022).

The disadvantage of SpArcFiRe is that it has a certain error in the annotation, as also noted in Appendix A in (Hayes et al.,, 2017). The Ganalyzer algorithm described in Section 2 allows to adjust the accuracy of the annotation by setting the minimum number of peaks required to make an annotation. If the number of peaks identified in the radial intensity plot is lower than the threshold, the galaxy is not used in the analysis. That leads to the rejection of a large number of galaxies. In the case of DECam, the initial number of galaxies is very high, and therefore even after rejecting a large number of galaxies the remaining galaxies make it a sufficiently large dataset to allow statistical analysis. SpArcFiRe, on the other hand, is far slower and has a certain error, but it also rejects a smaller number of galaxies. The use of SpArcFiRe also allows to use two different analysis methods.

Classification of a single 128 $\times$ 128 galaxy image requires $\sim$ 30 seconds when using a single core of a recent Intel Core-i7 processor. To reduce the response time, 100 cores were used to annotate the image data using SpArcFiRe. Figure 6 displays the RA distribution of the galaxies. As the figure shows, the galaxy population is not distributed uniformly in the sky.

As the figure shows, the distribution of SDSS galaxies in the sky is not uniform. Fortunately for this specific study, the population of SDSS galaxies is relatively dense around the Northern galactic pole. That allows to study the difference in brightness of galaxies that spin with or against the spin direction of the Milky Way.

The annotation provided a set of 273,055 galaxies with annotated spin directions. The SpArcFiRe method was then applied again after mirroring the galaxy images, providing a set of 273,346 galaxies. The slight differences between the results after mirroring the images is mentioned in (Hayes et al.,, 2017), and will be discussed later in this paper.

A first experiment was by just applying SpArcFiRe without any first step of selecting spiral galaxies. While the annotation of galaxies that are elliptical can add noise, it might be expected that the error in the annotation will be distributed equally between clockwise and counterclockwise galaxies. SpArcFiRe also does not force a certain spin direction, and can also annotate galaxies as not spinning in any identifiable direction. When SpArcFiRe is not able to identify the spin direction of the galaxy, . Table 8 shows the magnitude differences in the field of $60^{o}\times 60^{o}$ around the Northern galactic pole. The annotation process provided 55,223 galaxies spinning counterclockwise, and 55,051 spinning clockwise in that field. Because SpArcFiRe is not fully symmetric, the experiment was repeated after mirroring all galaxy images, and the results are shown in Table 9. The annotation of the mirrored images provided a dataset of 55,874 mirrored galaxies spinning clockwise and 54,488 mirrored galaxies spinning counterclockwise. The list of galaxies and their annotations as assigned by SpArcFiRe is available at https://people.cs.ksu.edu/~lshamir/data/sparcfire_data/.

Table 8: The g, r, and z exponential magnitudes of SDSS galaxies that spin with the Milky Way and galaxies that spin in the opposite direction compared to the Milky Way in the field centered around the North galactic pole.

Band	Mag	Mag	$\Delta Mag$	P
	cw	ccw		t-test
G	17.7652 $\pm$ 0.004	17.7558 $\pm$ 0.004	0.0094	0.035
R	17.0016 $\pm$ 0.003	16.9922 $\pm$ 0.003	0.0094	0.013
Z	16.449 $\pm$ 0.003	16.4357 $\pm$ 0.003	0.0132	0.001

Table 9: The g, r, and z exponential magnitudes of mirrored SDSS galaxies that spin with the Milky Way and galaxies that spin in the opposite direction compared to the Milky Way in the field centered around the North galactic pole.

Band	Mag	Mag	$\Delta Mag$	P
	cw	ccw		t-test
G	17.7576 $\pm$ 0.004	17.762 $\pm$ 0.004	-0.0044	0.21
R	16.9936 $\pm$ 0.003	17.0016 $\pm$ 0.003	-0.008	0.025
Z	16.4357 $\pm$ 0.003	16.4479 $\pm$ 0.003	-0.0122	0.002

As the tables show, despite the certain inaccuracy of SpArcFiRe, the analysis still shows differences in the brightness of galaxies spinning clockwise and galaxies spinning counterclockwise at around the galactic pole. As expected, mirroring the galaxy images showed inverse results.

SpArcFiRe is designed to analyze spiral galaxies (Hayes et al.,, 2017). To apply SpArcFiRe to spiral galaxies, a set of spiral galaxies was separated from the other galaxies by using the Ganalyzer method (Shamir,, 2011). As a model-driven method, the analysis is not based on any kind of machine learning, and therefore it is not subjected to possible biases in the training data or the learning process (Dhar and Shamir,, 2022). The simple “mechanical” nature of Ganalyzer allows it to be fully symmetric (Shamir, 2021b, ; Shamir, 2022c, ).

Table 10 shows the number of clockwise and counterclockwise galaxies in the SDSS data after selecting the spiral galaxies, limited to the $60^{o}\times 60^{o}$ part of the sky centered at the Northern galactic pole. That dataset contained 27,196 galaxies spinning clockwise and 27,671 galaxies spinning counterclockwise. Since SDSS footprint covers mostly the Northern hemisphere, the Southern galactic pole is outside of its footprint. According to Table 10, the results shows statistically significant differences between the brightness of galaxies that spin in opposite directions.

Table 10: The g, r, and z exponential magnitudes of SDSS galaxies annotated as spiral galaxies. The analysis is limited to galaxies in the

60^{o}\times 60^{o}

centered at the Northern galactic pole.

Band	Mag	Mag	$\Delta Mag$	P
	cw	ccw		t-test
G	17.7095 $\pm$ 0.005	17.6948 $\pm$ 0.005	0.0147	0.0376
R	16.9893 $\pm$ 0.004	16.9745 $\pm$ 0.004	0.0148	0.0089
Z	16.4564 $\pm$ 0.004	16.4393 $\pm$ 0.004	0.0171	0.0025

The SDSS galaxies used in this study have redshift, which allows to separate them to redshift ranges. Table 11 shows the same analysis, but when limiting the galaxies to $z<0.07$ . When limiting the redshift to 0.07, the dataset included 8,409 clockwise galaxies and 8,748 counterclockwise galaxies. The results show a larger difference in magnitude in that redshift range. That, however, is not necessarily of an astronomical meaning, and could be linked to the better ability of SpArcFiRe to annotate galaxies at lower redshift ranges. As the other experiments with SDSS galaxies, the results are in agreement with the results of the DECam galaxies shown in Section 3.

Table 11: The g, r, and z magnitudes of SDSS galaxies limited to

z<0.07

that spin in the opposite directions in the field centered around the North galactic pole.

Band	Mag	Mag	$\Delta Mag$	P
	cw	ccw		t-test
G	16.9437 $\pm$ 0.009	16.9192 $\pm$ 0.009	0.0245	0.027
R	16.4017 $\pm$ 0.009	16.3723 $\pm$ 0.009	0.0294	0.01
Z	15.9827 $\pm$ 0.009	15.9499 $\pm$ 0.009	0.0328	0.005

4.1 Analysis with crowdsourcing data from Galaxy Zoo 1

One of the previous attempts to annotate galaxies by their spin direction was done by crowdsourcing through the Galaxy Zoo 1 project (Lintott et al.,, 2008). According to Galaxy Zoo 1, anonymous volunteers used a web-based user interface to manually annotate galaxies by their shape. Among other features, the users were asked to annotate the spin direction of the galaxies. While not all annotations are expected to be correct, the majority of the votes is expected to provide a certain indication regarding the spin direction.

The Galaxy Zoo annotations can be used to perform an experiment similar to the experiments described above, but with galaxies annotated manually by a large number of volunteers. Fortunately, the $60^{o}\times 60^{o}$ part of the sky centered around the Northern galactic pole is fairly populated by galaxies that were annotated through Galaxy Zoo 1, and the majority of Galaxy Zoo annotated galaxies are concentrated around that part of the sky. That allows to obtain the profile of brightness differences between galaxies that were annotated by Galaxy Zoo to spin clockwise, compared to the brightness of Galaxy Zoo galaxies that were annotated as spinning counterclockwise.

The Galaxy Zoo 1 annotations were taken from the “zooVotes” table of SDSS DR8. The galaxies include only galaxies of which 60% or more of the voters agreed on their spiral nature and spin direction. That is, the field “p_cw” was greater or equal to 0.6 for galaxies that spin clockwise, and the field “p_acw” was greater or equal to 0.6 for galaxies that spin counterclockwise. As before, missing values or flag values were removed. That provided a dataset of 11,150 galaxies spinning clockwise, and 11,907 galaxies spinning counterclockwise. All galaxies are inside the $60^{o}\times 60^{o}$ region centered at the Northern galactic pole. Table 12 shows the brightness differences in the g, r, and z bands for the Galaxy Zoo galaxies. As the table shows, the differences between the brightness of galaxies spinning in opposite directions in the Northern galactic are noticeable also in the galaxies annotated by Galaxy Zoo. The corresponding part of the sky in the Southern galactic pole has merely a total of 2,005 annotated galaxies, and therefore analysis of the Southern galactic pole is not possible in the same manner it was done with the DECam data.

Table 12: The g, r, and z exponential magnitudes of SDSS galaxies annotated by Galaxy Zoo in the field centered around the North galactic pole.

Band	Mag	Mag	$\Delta Mag$	P
	cw	ccw		t-test
G	16.9765 $\pm$ 0.01	16.9579 $\pm$ 0.01	0.0186	0.09
R	16.4129 $\pm$ 0.01	16.3723 $\pm$ 0.01	0.0406	0.002
Z	15.9817 $\pm$ 0.01	15.9539 $\pm$ 0.01	0.0278	0.025

The Galaxy Zoo 1 defines a “superclean” annotation as an annotation that 95% of the annotators provided the same annotation. Table 13 shows the differences in brightness of galaxies in the $60^{o}\times 60^{o}$ region around the Northern galactic pole such that all annotations of the galaxies meet the “superclean” criterion. The requirement for higher agreement of the annotators can lead to cleaner annotations, but that comes on the expense of the size of the dataset. When using just galaxies on which 95% of the annotators agree, the total number of annotated galaxies is merely 4,065. The number of clockwise galaxies is 1875, and the number of galaxies annotated as spinning counterclockwise is 2190. The results also show that galaxies spinning counterclockwise around the North galactic pole are brighter. The results are not statistically significant, which can be attributed to the smaller number if galaxies that satisfy the higher annotation agreement threshold. But the difference observed in the “superclean” galaxies also does not conflict with the difference observed with the larger datasets.

Table 13: The g, r, and z magnitudes of SDSS galaxies annotated as “superclean” by Galaxy Zoo in the field centered around the North galactic pole.

Band	Mag	Mag	$\Delta Mag$	P
	cw	ccw		t-test
G	16.3496 $\pm$ 0.03	16.3122 $\pm$ 0.03	0.0374	0.189
R	15.7912 $\pm$ 0.03	15.7443 $\pm$ 0.03	0.0468	0.135
Z	15.377 $\pm$ 0.03	15.3235 $\pm$ 0.03	0.0535	0.104

The Galaxy Zoo annotations are known to be subjected to certain biases that are often difficult to fully profile (Hayes et al.,, 2017). The brightness differences observed with galaxies annotated by Galaxy Zoo can therefore be the results of some unknown bias where the volunteers tend to annotate brighter galaxies as galaxies rotating counterclockwise. These biases can be difficult to quantify and fully profile, and therefore the results when using the Galaxy Zoo annotations might not be sufficient to provide strong evidence of brightness differences. The agreement between the results of Galaxy Zoo and the results of DECam and SDSS can also be considered a coincidence. But the results of Galaxy Zoo also do not conflict with the results shown with the automatically annotated galaxies, and in fact are in good agreement with the other experiments. Whether the agreement is the result of an astronomical reason or a certain unidentified human bias is still a matter that is difficult to fully determine due to the complex nature of the possible human biases of the crowdsourcing-based annotations.

5 Analysis with Pan-STARRS data

A sky survey that covers more of the Southern sky than SDSS is Pan-STARRS. Like SDSS, Pan-STARRS covers mostly the Northern sky, but its footprint covers more of the Southern hemisphere compared to SDSS. Using a dataset of Pan-STARRS DR1 galaxies used in a previous study (Shamir, 2017b, ) provided the magnitude difference of 3,587 galaxies in the $60^{o}\times 60^{o}$ around the Southern galactic pole. The galaxies can be accessed at https://people.cs.ksu.edu/~lshamir/data/assym3/. The results show that in the part of the sky around the Southern galactic pole galaxies that spin clockwise are brighter than galaxies that spin counterclockwise. That difference is in agreement with the results of DECam for the Southern galactic pole. The results are shown in Table 14.

Table 14: The g, r, and z exponential magnitudes of Pan-STARRS galaxies at around the Southern galactic pole.

Band	Mag	Mag	T-test P
	cw	ccw
G	16.9066 $\pm$ 0.02	16.9972 $\pm$ 0.02	0.0014
R	16.3463 $\pm$ 0.02	16.4226 $\pm$ 0.02	0.007
Z	15.8408 $\pm$ 0.02	15.9087 $\pm$ 0.02	0.0164

6 HST data

As ground-based instruments, DECam, SDSS, and Pan-STARRS are subjected to the effect of the atmosphere. There is no known atmospheric effect that can effect galaxies differently based on their spin direction, and therefore the atmosphere is not expected to lead to such difference. To test empirically whether the difference is consistent also when imaging the galaxies without the effect of the atmosphere, we used galaxies imaged by the Hubble Space Telescope (HST). These results were shown initially in (Shamir, 2020a, ).

The galaxies used in this experiment were imaged by the Cosmic Evolution Survey (COSMOS) of HST. As the largest HST field, COSMOS (Scoville et al.,, 2007; Koekemoer et al.,, 2007; Capak et al.,, 2007) covers $\sim$ 2 square degrees, centered at ( $\alpha=150.119^{o}$ , $\delta=2.2058^{o}$ ). The initial list of objects included 114,630 COSMOS objects that are at least 5 $\sigma$ brighter than their background. Each galaxy image was separated from the F814W image by using the Montage (Berriman et al.,, 2004) tool. The images were annotated by the Ganalyzer algorithm (Shamir,, 2011), and then inspected manually. That led to a dataset of 2,607 galaxies that spin clockwise, and 2,515 galaxies that spin counterclockwise. The full details of the annotation process are provided in (Shamir, 2020a, ), and the annotated data can be accessed at http://people.cs.ksu.edu/~lshamir/data/assym_COSMOS/.

Table 15 shows the brightness in the g, r, and z filters of galaxies spinning in opposite directions. The magnitudes are the Subaru AB magnitudes (Capak et al.,, 2007). The comparison provides certain evidence that in the COSMOS field galaxies that spin counterclockwise are brighter than galaxies that spin clockwise. The COSMOS field is not aligned with neither the Northern nor the Southern galactic pole, but it is far closer to the Northern galactic pole. According to the other experiments described earlier in this paper, in the Northern galactic pole galaxies that spin counterclockwise are expected to be brighter. That observation is aligned with the results observed with the HST galaxies, reported in (Shamir, 2020a, ). The difference in the z band is not necessarily statistically significant, but the findings are aligned with the results shown by the other telescopes, and definitely do not conflict with DECam, SDSS and Pan-STARRS.

Table 15: The brightness of HST galaxies spinning in opposite directions in the COSMOS field.

Band	Mag cw	Mag ccw	$\Delta$ Mag	P (t-test)
G	23.131 $\pm$ 0.019	23.077 $\pm$ 0.019	0.054	0.023
R	22.266 $\pm$ 0.019	22.218 $\pm$ 0.02	0.048	0.045
Z	21.358 $\pm$ 0.017	21.323 $\pm$ 0.018	0.035	0.087

7 Reasons that can lead to differences in brightness

The differences in brightness between galaxies spinning in opposite directions cannot be determined by direct observation, but by analysis of a large number of galaxies. Large-scale analysis of a high number of galaxies to determine properties that are difficult to obtain with direct measurements is not a new practice, and is used in tasks such as weak gravitational lensing (Van Waerbeke et al.,, 2000; Wittman et al.,, 2000; Mandelbaum et al.,, 2006; Hirata et al.,, 2007; Abbott et al.,, 2016). The purpose of this section is to review the analysis and possible errors that can lead to the observation.

7.1 Incorrectly annotated galaxies

One of the key aspects of the analysis shown here is the annotation of the galaxies by their spin direction. Two different algorithms were used in this study, as well as manually annotated galaxies using crowdsourcing, all show similar results. For the computer-based annotations, the experiments were repeated after mirroring the galaxy images, leading to inverse results. Also, the brightness difference is inverse in the Northern galactic pole compared to the Southern galactic pole. A bias in the algorithm is expected to be consistent in both ends of the Galactic pole, rather than flip.

Also, if an algorithm that annotates the galaxies by their spin directions annotates some of the galaxies with wrong spin direction, the brightness difference $\Delta M$ at a certain part of the sky is determined by Equation 2

\Delta M=((1-e)\bar{M_{cw}}+e\bar{E_{cw}})-((1-e)\bar{M_{ccw}}+e\bar{E_{ccw}}),

(2)

where $\bar{M_{cw}}$ is the mean magnitude of galaxies spinning clockwise that are also annotated correctly by the classifier as galaxies spinning clockwise, $\bar{E_{cw}}$ is the mean magnitude of galaxies spinning counterclockwise but annotated incorrectly as spinning clockwise, and $e$ is the error rate of the annotation algorithm. The equation can be re-written as

\Delta M=\bar{M_{cw}}-\bar{M_{ccw}}+e(\bar{E_{cw}}-\bar{E_{ccw}}+\bar{M_{ccw}}-\bar{M_{cw}}).

(3)

Let $\vartheta=\bar{M_{cw}}-\bar{M_{ccw}}$ and $\varphi=\bar{E_{cw}}-\bar{E_{ccw}}$ . $\Delta M$ can be now expressed as $\Delta M=\vartheta+e(\vartheta-\varphi)$ . If the magnitude between clockwise and counterclockwise galaxies is different, it should be consistent for all galaxies, including galaxies that are annotated incorrectly. In that case, $\varphi=-\vartheta$ , and $\Delta M=\vartheta+e(-2\vartheta)$ . That shows that the $\Delta$ M that includes galaxies annotated incorrectly is smaller than $\vartheta$ . Therefore, a higher rate of error in the annotation $e$ will lead to a smaller $\Delta M$ . Therefore, error in the annotation can lead to lower difference in magnitude, but since $e\geq 0$ , it cannot lead to a higher difference.

7.2 Cosmic variance

Galaxies as observed from Earth are not distributed in the sky in a fully uniform manner, leading to subtle fluctuations in galaxy density known as “cosmic variance” (Driver and Robotham,, 2010; Moster et al.,, 2011). These small fluctuations in galaxy population density can affect measurements at different parts of the sky and different directions of observation (Kamionkowski and Loeb,, 1997; Camarena and Marra,, 2018; Keenan et al.,, 2020).

The probe used in this study is the brightness difference between galaxies imaged in the same part of the sky, by the same telescope, in the same exposure, and the same analysis methods. That is, anything that might affect the brightness of galaxies that spin with the Milky Way is also expected to affect galaxies spinning in the opposite direction. There is no attempt to compare magnitudes measured in two different parts of the sky, two different instruments, or even two different exposures. In all experiments the mean brightness of galaxies spinning in one direction is compared to the mean brightness of galaxies spinning in the opposite way such that all galaxies are in the exact same part of the sky. Any cosmic variance that might affect galaxies spinning with the Milky Way is expected to affect the mean magnitude of galaxies spinning in the opposite direction.

7.3 Bias in the hardware or photometric pipelines of digital sky surveys

Digital sky surveys are some of the more complex research instruments of our time. That complexity makes it very difficult to inspect every single part of these systems and ensure that no bias exists. At the same time, it is also difficult to propose a certain possible flaw that can lead to differences in the brightness of galaxies that spin in the same direction as the Milky Way and galaxies that spin in the opposite direction. Moreover, the difference in brightness flips between the Northern and Southern galactic poles, making it more difficult to propose an explanation based on a possible hardware or software flaw.

In this study, several different digital sky surveys were used, and the results are consistent across the different telescopes. While it is challenging to propose of a specific flaw in a digital sky survey that exhibits itself in such form in a single telescope, it is more difficult to think of such flaw in several unrelated sky surveys.

7.4 Atmospheric effect

Atmospheric effect might change the brightness of galaxies as observed from Earth, and can lead to differences in brightness observed in different parts of the sky. As also discussed in 7.2, the comparison between the magnitudes are done in the same part of the sky, and all galaxies were taken from the exact same frames and exposures. Therefore, all atmospheric effects that can change the magnitude of galaxies that spin in one direction are expected to change the magnitude of galaxies that spin in the opposite direction.

To completely eliminate the atmospheric effect, an experiment was done with data from Hubble Space Telescope. That experiment is described in Section 6. The results of that experiment are consistent with the results from the ground-based telescopes, providing another indication that the difference in brightness is not the result of the effect of the Earth’s atmosphere.

7.5 Spiral galaxies with leading arms

Although the vast majority of spiral galaxies have trailing arms, in some less common cases the arms of a spiral galaxy can be leading. For instance, a notable case of a galaxy with leading spirals arms is NGC 4622 (Freeman et al.,, 1991; Buta et al.,, 2003; Byrd et al.,, 2007). Assuming that the spin direction of a galaxy is driven by the perspective of the observer, the frequency of galaxies with leading arms among galaxies that spin in the same direction as the Milky Way is similar to the frequency of galaxies spinning in the opposite direction. In that case, galaxies with leading arms can be considered as galaxies that were annotated incorrectly, and subjected to the same analysis shown in Section 7.1.

8 Possible link to $H_{o}$ tension

The Hubble-Lemaitre constant ( $H_{o}$ ) tension (Wu and Huterer,, 2017; Mörtsell and Dhawan,, 2018; Bolejko,, 2018; Davis et al.,, 2019; Pandey et al.,, 2020; Camarena and Marra,, 2020; Di Valentino et al.,, 2021; Riess et al.,, 2022) is one of the most puzzling cosmological observations. In summary, the Hubble-Lemaitre constant $H_{o}$ determined by using Ia supernovae to measure the distance of galaxies is different from the constant measured with the cosmic microwave background radiation. Since both measure the same Universe, and assuming the Universe can only have one expansion rate, one of the explanations to the tension is that one of these probes has slight inaccuracies that lead to the different $H_{o}$ values. For instance, it has been suggested that Lorentz Relativistic Mass can affect the measurements using Ia supernovae (Haug,, 2022).

Hubble-Lemaitre constant can be determined by comparing the velocity of galaxies relative to their distance, such that the distance is determined by using Ia supernovae. Ia supernovae have an expected absolute magnitude, and therefore the apparent magnitude of an Ia supernova as observed from Earth can be used to determine the distance of the galaxy from Earth.

Supernovae are explosions of stars, and therefore a supernova rotates with the galaxy that the star was part of. The magnitude of the Ia supernova is measured from Earth, which also rotates with the Milky Way galaxy at around 220 km $\cdot$ sec ^-1. If the rotation of the galaxies that host Ia supernovae compared to the rotation of the Milky Way can affect the apparent magnitude of the supernova, that can lead to a different distance metrics from Ia supernovae that depends on the rotation of the galaxy compared to the rotation of the Milky Way. That is, because not all supernovae used in the measurements are located around the galactic pole and spin in the same direction as the Milky Way, their apparent magnitude might seem slightly different to an Earth based observer, leading to a slight change to the measured Hubble-Lemaitre constant. Because the rotational velocity of a galaxy correlates with the galaxy type, the link between rotational velocity and $H_{o}$ can be related to previous reports on correlation between $H_{o}$ and the type of the Ia supernova host galaxy (Khetan et al.,, 2021). Other studies suggested a link between Ia supernova and the properties of its host galaxies (Meldorf et al.,, 2022; Dixon et al.,, 2022).

An experiment that would test that assumption can be made by computing the Hubble-Lemaitre constant by using only Ia supernovae hosted by galaxies that rotate in the same direction as the Milky Way. Such galaxies can be from both the Northern and Southern hemisphere, such that the galaxies are located around the galactic pole. That would require a certain number of Ia supernovae located around the galactic pole, and galaxies spinning in the same direction as the Milky Way. If the measurement of the Hubble-Lemaitre constant when using galaxies that rotate with the Milky Way provides a different result than when using all galaxies, that can provide an indication that the spin direction affects the determined Hubble-Lemaitre constant. If the result is also close to the Hubble-Lemaitre constant as determined by the CMB radiation, that can also explain the $H_{o}$ tension, and might also explain other observation made with Ia supernovae as distance candles.

To perform a simple test, we used the code and data provided by Khetan et al., (2021) for determining the $H_{o}$ constant. Khetan et al., (2021) use a set of 140 Ia supernovae, calibrated with Pan-STARRS. The calibration is done using two sets. The primary one is a set of 24 SBF (Khetan et al.,, 2021) Ia supernovae. Additionally, a set of 19 Ia SH0ES (Riess et al.,, 2019) supernovae is also used. The full description of the data and calibration is provided in (Khetan et al.,, 2021).

In addition to using the 140 supernovae as done in (Khetan et al.,, 2021), we also separate a subset of the 140 supernovae into supernovae within 45^o from the Southern galactic pole and their host galaxies spin clockwise, or within 45^o from the Northern galactic pole and their host galaxies spin counterclockwise. That provided a list of 26 supernovae. Five of these supernovae had redshift of $z<0.02$ , and were excluded from the analysis as was done in (Khetan et al.,, 2021). The 21 supernovae are SN2005iq, SN2008Y, SN2004L, SN2006cq, SN2006or, SN2008bz, SN2005hc, SN2005eq, SN2008ar, SN2001ah, SN2006et, SN2002G, SN2005lu, SN1996bl, SN1999ef, SN2009na, SN2009D, SN2007O, SN1994Q, SN2006ac, SN2006cj.

When computing $H_{o}$ using the 140 supernovae and the SBF calibration, the $H_{o}$ constant is 69.070 km/s/Mpc. That was done by using the code in the file Hierarchical_noHM_SBF ³³3https://github.com/nanditakhetan/SBF_SNeIa_H0. The 3% error range of (64.747, 73.622). When using the subset of 21 supernovae, the computed $H_{o}$ increases to 69.551 km/s/Mpc, and 3% error range of (63.880, 75.787). That change makes the $H_{o}$ closer to the $H_{o}$ measured with the CMB. Due to the large error margins the change is not statistically significant, but it is aligned with the contention that normalization of the spin directions can reduce the Hubble tension.

The observed $H_{o}$ when using the 21 supernovae with normalized spin and SBF calibration is not the same as the $H_{o}$ observed with CMB, and therefore does not provide an immediate explanation to the $H_{o}$ tension. That can be explained in several ways. The first is that the reason proposed here is not the real cause of the $H_{o}$ tension, and there are other factors that affect the measurements. Another reason is that the Ia supernovae used here are within certain proximity to the galactic pole, but not exactly on it. Also, the declination of these galaxies is not zero, which can also lead to a certain Doppler shift effect. A more suitable future experiment would require a larger number of Ia supernovae that are exactly on the galactic pole, and are full face-on galaxies. Still, the $H_{o}$ observed with the CMB radiation is within the error range of the $H_{o}$ determined here.

9 Conclusions

The results show that in the fields around the galactic pole galaxies that spin clockwise have a different brightness than galaxies that spin counterclockwise. Such differences are expected due to relativistic beaming of galaxies that spin in the opposite direction to that of the Milky Way. The inverse difference in the opposite ends of the galactic pole shows that the observations in the both ends are in agreement with the spin direction of the Milky Way. Clearly, a galaxy that seem to spin clockwise in the Northern galactic pole spins in the same direction as galaxies that seem to spin counterclockwise in the Southern galactic pole, and vice versa. The control fields that are 90^o from the galactic pole show no significant difference between galaxies spinning in opposite directions, which provides a certain indication of a correlation between the galactic pole and the magnitude difference. The contention that relativistic beaming can lead to a certain statistical asymmetry when observing a population of galaxies is not unexpected (Alam et al.,, 2017).

Future and more powerful telescopes such as the Vera Rubin Observatory will allow better profiling of such difference. In case the maximum magnitude difference is greater than the maximum expected difference under optimal conditions, that observation can be related to modified Newtonian dynamics, or to relativistic beaming of gravity as an explanation to the galaxy rotation curve anomaly Blake, (2021). It can also be related to the observation of disagreement between the observed and expected velocity of halo spin Libeskind et al., (2013).

The observed difference between the magnitude of galaxies that spin in opposite directions had also been observed in previous studies Shamir, (2016); Shamir, 2017b ; Shamir, 2017c ; Shamir, 2020a , showing differences between galaxies that spin in opposite directions in the same field. These studies were based on far smaller datasets collected by sky surveys that did not cover the fields around both galactic poles. The data collected by DECam and available through the DESI Legacy Survey allows direct comparison of the differences in brightness between the two ends of the galactic pole. These differences can be related to the effect of relativistic beaming, but further research will be required with more powerful instruments to quantify and profile the magnitude difference.

9.1 Large-scale structure explanation

Another possible explanation to the observation can be an anomaly in the large-scale structure of the Universe. That is, the axis observed around the galactic pole is not the result of differences in the galaxy brightness as observed from Earth, but the result of the alignment in the spin directions of galaxies in the Universe. That explanation requires modification to the standard cosmological models, which rely on the assumption that the Universe is homogeneous and isotropic, an assumption defined as the Cosmological Principle.

While the Cosmological Principle is a common working assumption for most cosmological models, it has not been fully proven. In fact, multiple probes have shown evidence of violation of the cosmological principle (Aluri et al.,, 2022). Perhaps the most notable probe is the cosmic microwave background radiation, also exhibiting a cosmological-scale axis (Abramo et al.,, 2006; Mariano and Perivolaropoulos,, 2013; Land and Magueijo,, 2005; Ade et al.,, 2014; Santos et al.,, 2015; Gruppuso et al.,, 2018; Yeung and Chu,, 2022). It has been suggested that the axis exhibited by the cosmic microwave background radiation agrees with other axes formed by probes such as dark energy and dark flow (Mariano and Perivolaropoulos,, 2013). Other anomalies related to the cosmic microwave background radiation are the quandrupole-octopole alignment (Schwarz et al.,, 2004; Ralston and Jain,, 2004; Copi et al.,, 2007, 2010, 2015), the asymmetry between hemispheres (Eriksen et al.,, 2004; Land and Magueijo,, 2005; Akrami et al.,, 2014), and the point-parity asymmetry (Kim and Naselsky, 2010b, ; Kim and Naselsky, 2010a, ). Another related observation is the CMB cold spot (Cruz et al.,, 2007; Masina and Notari,, 2009; Vielva,, 2010; Mackenzie et al.,, 2017; Farhang and Movahed,, 2021). It has also been suggested that the isotropy observed with the CMB radiation is not statistically significant (Bennett et al.,, 2011).

In addition to the CMB, probes that show anisotropy include radio sources (Ghosh et al.,, 2016; Tiwari and Jain,, 2015; Tiwari and Nusser,, 2016; Singal,, 2019; Marcha and Browne,, 2021), LX-T scaling (Migkas et al.,, 2020), short gamma ray bursts (Mészáros,, 2019), acceleration rates (Perivolaropoulos,, 2014; Migkas et al.,, 2021; Krishnan et al.,, 2022), Ia supernova (Javanmardi et al.,, 2015; Lin et al.,, 2016), distribution of galaxy morphology types (Javanmardi and Kroupa,, 2017), dark energy (Adhav et al.,, 2011; Adhav,, 2011; Perivolaropoulos,, 2014; Colin et al.,, 2019), fine structure constant (Webb et al.,, 2011), galaxy motion (Skeivalas et al.,, 2021), $H_{o}$ (Luongo et al.,, 2022), polarization of quasars (Hutsemekers,, 1998; Hutsemékers et al.,, 2005; Secrest et al.,, 2021; Zhao and Xia,, 2021; Semenaite et al.,, 2021), and cosmic rays (Sommers,, 2001; Deligny and Salamida,, 2013; Aab et al.,, 2017, 2019). It has also been shown that the large-scale distribution of galaxies in the Universe is not random (Jones et al.,, 2005), and could have a preferred direction (Longo,, 2011; Shamir,, 2012; Shamir, 2019a, ; Shamir, 2020c, ; Shamir, 2020b, ; Shamir, 2021b, ; Shamir, 2022c, ; Shamir, 2022b, ; Philcox,, 2022; Hou et al.,, 2022). These probes might not agree with the standard models (Pecker,, 1997; Perivolaropoulos,, 2014; Bull et al.,, 2016; Velten and Gomes,, 2020; Krishnan et al.,, 2022, 2021; Luongo et al.,, 2022; Colgáin,, 2022; Abdalla et al.,, 2022)

The contention of a cosmological-scale axis agrees with cosmological theories that shift from the standard models. For instance, black hole cosmology (Pathria,, 1972; Stuckey,, 1994; Easson and Brandenberger,, 2001; Seshavatharam,, 2010; Popławski,, 2010; Christillin,, 2014; Dymnikova,, 2019; Chakrabarty et al.,, 2020; Popławski,, 2021; Seshavatharam and Lakshminarayana,, 2022; Gaztanaga, 2022a, ; Gaztanaga, 2022b, ) is a cosmological theory aligned with the contention of the existence of a large-scale axis. Black holes are born from the collapse of a star, and since stars spin black holes also spin (Gammie et al.,, 2004; Takahashi,, 2004; Volonteri et al.,, 2005; McClintock et al.,, 2006; Mudambi et al.,, 2020; Reynolds,, 2021). Supermassive black holes are also expected to spin (Montero et al.,, 2012), and observations of supermassive black holes showed that supermassive black holes spin (Reynolds,, 2019). An early example of such observation is the spin of the supermassive black hole of NGC 1365 (Reynolds,, 2013). Since black holes spin, if the Universe is the interior of a back hole it is expected to spin around a major axis inherited from the black hole. That observation is aligned with the agreement between the Hubble radius of the Universe and the Schwarzschild radius of a black hole such that the mass of the black hole is the mass of the Universe (Christillin,, 2014). Black hole cosmology is a theory under the category of multiverse (Carr and Ellis,, 2008; Hall and Nomura,, 2008; Antonov,, 2015; Garriga et al.,, 2016), which is one of the first cosmological paradigms (Trimble,, 2009; Kragh,, 2009).

In addition to black hole cosmology, several other cosmological theories that assume the existence of a cosmological scale axis have been proposed. These theories include ellipsoidal universe (Campanelli et al.,, 2006, 2007, 2011; Gruppuso,, 2007; Cea,, 2014), flat space cosmology (Tatum et al., 2015a, ; Tatum et al., 2015b, ; Tatum et al.,, 2018; Azarnia et al.,, 2021), geometric inflation (Arciniega et al., 2020a, ; Edelstein et al.,, 2020; Arciniega et al., 2020b, ; Jaime,, 2021), supersymmetric flows (Rajpoot and Vacaru,, 2017), and rotating universe (Gödel,, 1949; Ozsváth and Schücking,, 1962; Ozsvath and Schücking,, 2001; Su and Chu,, 2009; Sivaram and Arun,, 2012; Chechin,, 2016, 2017; Seshavatharam and Lakshminarayana,, 2020; Campanelli,, 2021). Other theories are double inflation (Feng and Zhang,, 2003), f( $\mathscr{R}$ , $\mathscr{L}_{m})$ gravity (Kavya et al.,, 2022), contraction prior to inflation (Piao et al.,, 2004), primordial anisotropic vacuum pressure (Rodrigues,, 2008), moving dark energy (Beltran Jimenez and Maroto,, 2007), multiple vacua (Piao,, 2005), and spinor-driven inflation (Bohmer and Mota,, 2008). While these theories shift from the standard cosmological models, they provide an explanation to an observed axis of a cosmological-scale. Since the standard model has not been fully proven, alternative theories to the standard cosmology should also be considered.

10 Discussion

Despite decades of intensive research efforts, the physical nature of galaxy rotation is still an unsolved question. The common possible explanations are that the distribution and quantity of the mass of galaxies does not fit its physical properties (dark matter), or that the laws of physics are different when applied to galaxies. This paper proposes the contention that the rotational velocity of the galaxy does not fit its physical properties, and corresponds to a much higher rotational velocity. The explanation is driven by the observation that galaxies that spin in the same direction as the Milky Way have different brightness compared to galaxies that spin in the opposite direction.

While such difference in brightness can be explained by Doppler shift, the difference is expected to be small. The observed difference is far greater than the expected difference, and it is observable with Earth-based telescopes. A possible explanation is that the physics of galaxy rotation corresponds to a far higher rotational velocity than the observed velocity. While that explanation is physically provocative, the physics of galaxy rotation is still unexplained, and does not follow known or proven physical theories. For instance, the absence of Keplerian velocity decrease in the galaxy rotation curve was ignored for several decades, also because it did not agree with the physical theories (Rubin,, 2000).

The tension between galaxy rotational velocity and its physical properties is one of many other possible explanations to the observation of different brightness for galaxies spinning in opposite directions. Another possible explanation discussed here is a possible anomaly in the large-scale structure. In that case, the difference in brightness is not driven by the perspective of an Earth-based observer, but reflects the real structure of the Universe. Other explanations not considered in this paper can also be possible.

The link between the rotational velocity of a galaxy and the apparent brightness of its objects can also be related to measurements made with Ia supernovae. Measurements with Ia supernovae have provided unexpected results, and have been shown to be in disagreement with other measurements. For instance, the $H_{o}$ tension suggests that the CMB or Ia supernovae do not match, and since both are applied to the same Universe it can be assumed that one of these measurements is inaccurate. If the brightness of an Ia supernovae depends on the rotational velocity of the galaxy that hosts it, and the galaxy may not necessarily spin in the same direction as the Milky Way, that can lead to slight changes in the apparent magnitude of the supernovae. Because the distance of an Ia supernovae is determined from its brightness, unexpected changes in the apparent magnitude can lead to a slightly different distance, and consequently to a slightly different $H_{o}$ . The initial observation of the accelerated expansion of the Universe was also made with Ia supernovae, and such changes in brightness can also have a certain impact on these results.

Acknowledgments

This study was supported in part by NSF grants AST-1903823 and IIS-1546079.

References

Aab et al., (2017) Aab, A., Abreu, P., Aglietta, M., Al Samarai, I., Albuquerque, I., Allekotte, I., Almela, A., Castillo, J. A., Alvarez-Muñiz, J., Anastasi, G. A., et al. (2017). Observation of a large-scale anisotropy in the arrival directions of cosmic rays above 8 $\times$ 1018 ev. Science, 357(6357):1266–1270.
Aab et al., (2019) Aab, A., Abreu, P., Aglietta, M., Albuquerque, I., Albury, J. M., Allekotte, I., Almela, A., Castillo, J. A., Alvarez-Muñiz, J., Anastasi, G. A., et al. (2019). Probing the origin of ultra-high-energy cosmic rays with neutrinos in the eev energy range using the pierre auger observatory. Journal of Cosmology and Astroparticle Physics, 2019(10):022.
Abbott et al., (2016) Abbott, T., Abdalla, F., Allam, S., Amara, A., Annis, J., Armstrong, R., Bacon, D., Banerji, M., Bauer, A., Baxter, E., et al. (2016). Cosmology from cosmic shear with dark energy survey science verification data. Physical Review D, 94(2):022001.
Abdalla et al., (2022) Abdalla, E., Abellán, G. F., Aboubrahim, A., Agnello, A., Akarsu, Ö., Akrami, Y., Alestas, G., Aloni, D., Amendola, L., Anchordoqui, L. A., et al. (2022). Cosmology intertwined: A review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies. Journal of High Energy Astrophysics.
Abramo et al., (2006) Abramo, L. R., Sodré Jr, L., and Wuensche, C. A. (2006). Anomalies in the low cmb multipoles and extended foregrounds. Physical Review D, 74(8):083515.
Ade et al., (2014) Ade, P. A., Aghanim, N., Armitage-Caplan, C., Arnaud, M., Ashdown, M., Atrio-Barandela, F., Aumont, J., Baccigalupi, C., Banday, A. J., Barreiro, R., et al. (2014). Planck 2013 results. xxiii. isotropy and statistics of the cmb. Astronomy & Astrophysics, 571:A23.
Adhav, (2011) Adhav, K. (2011). Lrs bianchi type-i universe with anisotropic dark energy in lyra geometry. International Journal of Astronomy and Astrophysics, 1(4):204–209.
Adhav et al., (2011) Adhav, K., Bansod, A., Wankhade, R., and Ajmire, H. (2011). Kantowski-sachs cosmological models with anisotropic dark energy. Open Physics, 9(4):919–925.
Akrami et al., (2014) Akrami, Y., Fantaye, Y., Shafieloo, A., Eriksen, H., Hansen, F. K., Banday, A. J., and Górski, K. M. (2014). Power asymmetry in wmap and planck temperature sky maps as measured by a local variance estimator. ApJL, 784(2):L42.
Alam et al., (2017) Alam, S., Croft, R. A., Ho, S., Zhu, H., and Giusarma, E. (2017). Relativistic effects on galaxy redshift samples due to target selection. Monthyl Notices of the Royal Astronomical Society, 471(2):2077–2087.
Alhassan et al., (2019) Alhassan, J. A., Ubachukwu, A. A., Odo, F. C., and Onuchukwu, C. C. (2019). Relativistic beaming effects and structural asymmetries in highly asymmetric double radio sources. Revista Mexicana de Astronomía y Astrofísica, 55(2):151–159.
Aluri et al., (2022) Aluri, P. K., Cea, P., Chingangbam, P., Chu, M.-C., Clowes, R. G., Hutsemékers, D., Kochappan, J. P., Krasiński, A., Lopez, A. M., Liu, L., Martens, N. C. M., Martins, C. J. A. P., Migkas, K., Colgáin, E. ., Pranav, P., Shamir, L., Singal, A. K., Sheikh-Jabbari, M. M., Wagner, J., Wang, S.-J., Wiltshire, D. L., Yeung, S., Yin, L., and Zhao, W. (2022). Is the observable universe consistent with the cosmological principle? arXiv, page 2207.05765.
Antonov, (2015) Antonov, A. A. (2015). Hidden multiverse. International Journal of Advanced Research in Physical Science, 2(1):25–32.
(14) Arciniega, G., Bueno, P., Cano, P. A., Edelstein, J. D., Hennigar, R. A., and Jaime, L. G. (2020a). Geometric inflation. PLB, 802:135242.
(15) Arciniega, G., Edelstein, J. D., and Jaime, L. G. (2020b). Towards geometric inflation: the cubic case. PLB, 802:135272.
Arun et al., (2017) Arun, K., Gudennavar, S., and Sivaram, C. (2017). Dark matter, dark energy, and alternate models: A review. Advances in Space Research, 60(1):166–186.
Azarnia et al., (2021) Azarnia, S., Fareghbal, R., Naseh, A., and Zolfi, H. (2021). Islands in flat-space cosmology. Physical Review D, 104(12):126017.
Babcock, (1939) Babcock, H. W. (1939). The rotation of the andromeda nebula. Lick Observatory Bulletin, 19:41–51.
Beltran Jimenez and Maroto, (2007) Beltran Jimenez, J. and Maroto, A. L. (2007). Cosmology with moving dark energy and the cmb quadrupole. Physical Review D, 76(2):023003.
Bennett et al., (2011) Bennett, C., Hill, R., Hinshaw, G., Larson, D., Smith, K., Dunkley, J., Gold, B., Halpern, M., Jarosik, N., Kogut, A., et al. (2011). Seven-year wilkinson microwave anisotropy probe (wmap*) observations: Are there cosmic microwave background anomalies? ApJS, 192(2):17.
Berriman et al., (2004) Berriman, G., Good, J., Laity, A., Bergou, A., Jacob, J., Katz, D., Deelman, E., Kesselman, C., Singh, G., Su, M.-H., et al. (2004). Montage: a grid enabled image mosaic service for the national virtual observatory. In Astronomical Data Analysis Software and Systems (ADASS) XIII, volume 314, page 593.
Bertone and Tait, (2018) Bertone, G. and Tait, T. M. (2018). A new era in the search for dark matter. Nature, 562(7725):51–56.
Blake, (2021) Blake, B. C. (2021). Relativistic beaming of gravity and the missing mass problem. Bulletin of the American Physical Society, page B17.00002.
Bohmer and Mota, (2008) Bohmer, C. G. and Mota, D. F. (2008). Cmb anisotropies and inflation from non-standard spinors. Physics Letters B, 663(3):168–171.
Bolejko, (2018) Bolejko, K. (2018). Emerging spatial curvature can resolve the tension between high-redshift cmb and low-redshift distance ladder measurements of the hubble constant. Physical Review D, 97(10):103529.
Bull et al., (2016) Bull, P., Akrami, Y., Adamek, J., Baker, T., Bellini, E., Jimenez, J. B., Bentivegna, E., Camera, S., Clesse, S., Davis, J. H., et al. (2016). Beyond $\lambda$ cdm: Problems, solutions, and the road ahead. Physics of the Dark Universe, 12:56–99.
Buta et al., (2003) Buta, R. J., Byrd, G. G., and Freeman, T. (2003). The ringed spiral galaxy ngc 4622. i. photometry, kinematics, and the case for two strong leading outer spiral arms. Astronomical Journal, 125(2):634.
Byrd and Howard, (2019) Byrd, G. and Howard, S. (2019). Ngc 4622: Unusual spiral density waves and calculated disk surface density. Journal of the Washington Academy of Sciences, 105(3):1–12.
Byrd and Howard, (2021) Byrd, G. and Howard, S. (2021). Spiral galaxies when disks dominate their halos (using arm pitches and rotation curves). Journal of the Washington Academy of Sciences, 107(1):1.
Byrd et al., (2007) Byrd, G. G., Freeman, T., Howard, S., and Buta, R. J. (2007). The ringed spiral galaxy ngc4622. ii. an independent determination that the two outer arms lead. Astronomical Journal, 135(1):408.
Camarena and Marra, (2018) Camarena, D. and Marra, V. (2018). Impact of the cosmic variance on h 0 on cosmological analyses. Physical Review D, 98(2):023537.
Camarena and Marra, (2020) Camarena, D. and Marra, V. (2020). Local determination of the hubble constant and the deceleration parameter. Physical Review Research, 2(1):013028.
Campanelli, (2021) Campanelli, L. (2021). A conjecture on the neutrality of matter. Foundations of Physics, 51:56.
Campanelli et al., (2011) Campanelli, L., Cea, P., Fogli, G., and Tedesco, L. (2011). Cosmic parallax in ellipsoidal universe. Modern Physics Letters A, 26(16):1169–1181.
Campanelli et al., (2006) Campanelli, L., Cea, P., and Tedesco, L. (2006). Ellipsoidal universe can solve the cosmic microwave background quadrupole problem. PRL, 97(13):131302.
Campanelli et al., (2007) Campanelli, L., Cea, P., and Tedesco, L. (2007). Cosmic microwave background quadrupole and ellipsoidal universe. Physical Review D, 76(6):063007.
Capak et al., (2007) Capak, P., Aussel, H., Ajiki, M., McCracken, H., Mobasher, B., Scoville, N., Shopbell, P., Taniguchi, Y., Thompson, D., Tribiano, S., et al. (2007). The first release cosmos optical and near-ir data and catalog. Astrophysical Journal Supplement Series, 172(1):99.
Capozziello and De Laurentis, (2012) Capozziello, S. and De Laurentis, M. (2012). The dark matter problem from f (r) gravity viewpoint. Annalen der Physik, 524(9-10):545–578.
Carr and Ellis, (2008) Carr, B. and Ellis, G. (2008). Universe or multiverse? Astronomy & Geophysics, 49(2):2–29.
Cea, (2014) Cea, P. (2014). The ellipsoidal universe in the planck satellite era. Monthly Notices of the Royal Astronomical Society, 441(2):1646–1661.
Chadwick et al., (2013) Chadwick, E. A., Hodgkinson, T. F., and McDonald, G. S. (2013). Gravitational theoretical development supporting mond. Physical Review D, 88(2):024036.
Chakrabarty et al., (2020) Chakrabarty, H., Abdujabbarov, A., Malafarina, D., and Bambi, C. (2020). A toy model for a baby universe inside a black hole. European Physical Journal C, 80(1909.07129):1–10.
Chechin, (2016) Chechin, L. (2016). Rotation of the universe at different cosmological epochs. Astronomy Reports, 60(6):535–541.
Chechin, (2017) Chechin, L. (2017). Does the cosmological principle exist in the rotating universe? Gravitation and Cosmology, 23(4):305–310.
Christillin, (2014) Christillin, P. (2014). The machian origin of linear inertial forces from our gravitationally radiating black hole universe. The European Physical Journal Plus, 129(8):1–3.
Cohen et al., (2007) Cohen, M., Lister, M., Homan, D., Kadler, M., Kellermann, K., Kovalev, Y., and Vermeulen, R. (2007). Relativistic beaming and the intrinsic properties of extragalactic radio jets. Astrophysical Journal, 658(1):232.
Colgáin, (2022) Colgáin, E. Ó. (2022). Probing the anisotropic universe with gravitational waves. arXiv:2203.03956.
Colin et al., (2019) Colin, J., Mohayaee, R., Rameez, M., and Sarkar, S. (2019). Evidence for anisotropy of cosmic acceleration. Astronomy & Astrophysics, 631:L13.
Copi et al., (2007) Copi, C. J., Huterer, D., Schwarz, D. J., and Starkman, G. D. (2007). Uncorrelated universe: statistical anisotropy and the vanishing angular correlation function in wmap years 1–3. Physical Review D, 75(2):023507.
Copi et al., (2010) Copi, C. J., Huterer, D., Schwarz, D. J., and Starkman, G. D. (2010). Large-angle anomalies in the cmb. Advances in Astronomy, 2010.
Copi et al., (2015) Copi, C. J., Huterer, D., Schwarz, D. J., and Starkman, G. D. (2015). Large-scale alignments from wmap and planck. Monthly Notices of the Royal Astronomical Society, 449(4):3458–3470.
Cruz et al., (2007) Cruz, M., Cayon, L., Martinez-Gonzalez, E., Vielva, P., and Jin, J. (2007). The non-gaussian cold spot in the 3-year wmap data. Astrophysical Journal, 655(11).
Davis and Hayes, (2014) Davis, D. R. and Hayes, W. B. (2014). SpArcFiRe: Scalable Automated Detection of Spiral Galaxy Arm Segments. Astrophysical Journal, 790(2):87.
Davis et al., (2019) Davis, T. M., Hinton, S. R., Howlett, C., and Calcino, J. (2019). Can redshift errors bias measurements of the hubble constant? Monthly Notices of the Royal Astronomical Society, 490(2):2948–2957.
De Blok and McGaugh, (1998) De Blok, W. and McGaugh, S. (1998). Testing modified newtonian dynamics with low surface brightness galaxies: rotation curve fits. Astrophysical Journal, 508(1):132.
De Vaucouleurs, (1959) De Vaucouleurs, G. (1959). General physical properties of external galaxies. In Astrophysik IV: Sternsysteme/Astrophysics IV: Stellar Systems, pages 311–372. Springer.
Deligny and Salamida, (2013) Deligny, O. and Salamida, F. (2013). Searches for large-scale anisotropies of cosmic rays: Harmonic analysis and shuffling technique. Astroparticle Physics, 46:40–49.
Dey et al., (2019) Dey, A., Schlegel, D. J., Lang, D., Blum, R., Burleigh, K., Fan, X., Findlay, J. R., Finkbeiner, D., Herrera, D., Juneau, S., et al. (2019). Overview of the desi legacy imaging surveys. Astronomical Journal, 157(5):168.
Dhar and Shamir, (2022) Dhar, S. and Shamir, L. (2022). Systematic biases when using deep neural networks for annotating large catalogs of astronomical images. Astronomy and Computing, 38:100545.
Di Valentino et al., (2021) Di Valentino, E., Mena, O., Pan, S., Visinelli, L., Yang, W., Melchiorri, A., Mota, D. F., Riess, A. G., and Silk, J. (2021). In the realm of the hubble tension—a review of solutions. Classical and Quantum Gravity, 38(15):153001.
Díaz-Saldaña et al., (2018) Díaz-Saldaña, I., López-Domínguez, J., and Sabido, M. (2018). On emergent gravity, black hole entropy and galactic rotation curves. Physics of the Dark Universe, 22:147–151.
Dixon et al., (2022) Dixon, M., Lidman, C., Mould, J., Kelsey, L., Brout, D., Möller, A., Wiseman, P., Sullivan, M., Galbany, L., Davis, T. M., Vincenzi, M., Scolnic, D., Lewis, G. F., Smith, M., Kessler, R., Duffy, A., Taylor, E. N., Flynn, C., Abbott, T. M. C., Aguena, M., Allam, S., Andrade-Oliveira, F., Annis, J., Asorey, J., Bertin, E., Bocquet, S., Brooks, D., Burke, D. L., Carnero Rosell, A., Carollo, D., Carrasco Kind, M., Carretero, J., Costanzi, M., da Costa, L. N., Pereira, M. E. S., Doel, P., Everett, S., Ferrero, I., Flaugher, B., Friedel, D., Frieman, J., García-Bellido, J., Gatti, M., Gerdes, D. W., Glazebrook, K., Gruen, D., Gschwend, J., Gutierrez, G., Hinton, S. R., Hollowood, D. L., Honscheid, K., Huterer, D., James, D. J., Kuehn, K., Kuropatkin, N., Malik, U., March, M., Menanteau, F., Miquel, R., Morgan, R., Nichol, B., Ogando, R. L. C., Palmese, A., Paz-Chinchón, F., Pieres, A., Plazas Malagón, A. A., Rodriguez-Monroy, M., Romer, A. K., Sanchez, E., Scarpine, V., Sevilla-Noarbe, I., Soares-Santos, M., Suchyta, E., Tarle, G., To, C., Tucker, B. E., Tucker, D. L., and Varga, T. N. (2022). Using host galaxy spectroscopy to explore systematics in the standardization of type ia supernovae. Monthly Notices of the Royal Astronomical Society, 517(3):4291–4304.
Dodelson, (2011) Dodelson, S. (2011). The real problem with mond. International Journal of Modern Physics D, 20(14):2749–2753.
Dojcsak and Shamir, (2014) Dojcsak, L. and Shamir, L. (2014). Quantitative analysis of spirality in elliptical galaxies. New Astronomy, 28:1–8.
Donato et al., (2009) Donato, F., Gentile, G., Salucci, P., Frigerio Martins, C., Wilkinson, M., Gilmore, G., Grebel, E., Koch, A., and Wyse, R. (2009). A constant dark matter halo surface density in galaxies. Monthly Notices of the Royal Astronomical Society, 397(3):1169–1176.
Driver and Robotham, (2010) Driver, S. P. and Robotham, A. S. (2010). Quantifying cosmic variance. Monthyl Notices of the Royal Astronomical Society, 407(4):2131–2140.
Dymnikova, (2019) Dymnikova, I. (2019). Universes inside a black hole with the de sitter interior. Universe, 5(5):111.
Easson and Brandenberger, (2001) Easson, D. A. and Brandenberger, R. H. (2001). Universe generation from black hole interiors. Journal of High Energy Physics, 2001(06):024.
Edelstein et al., (2020) Edelstein, J. D., Rodríguez, D. V., and López, A. V. (2020). Aspects of geometric inflation. JCAP, 2020(12):040.
Eriksen et al., (2004) Eriksen, H. K., Hansen, F. K., Banday, A. J., Gorski, K. M., and Lilje, P. B. (2004). Asymmetries in the cosmic microwave background anisotropy field. Astrophysical Journal, 605(1):14.
Falcon, (2021) Falcon, N. (2021). A large-scale heuristic modification of newtonian gravity as an alternative approach to dark energy and dark matter. Journal of Astrophysics and Astronomy, 42(2):1–13.
Farhang and Movahed, (2021) Farhang, M. and Movahed, S. (2021). Cmb cold spot in the planck light. Astrophysical Journal, 906(1):41.
Farnes, (2018) Farnes, J. S. (2018). A unifying theory of dark energy and dark matter: Negative masses and matter creation within a modified $\lambda$ cdm framework. Astronomy & Astrophysics, 620:A92.
Feng and Zhang, (2003) Feng, B. and Zhang, X. (2003). Double inflation and the low cmb quadrupole. Physics Letters B, 570(3-4):145–150.
Flaugher et al., (2012) Flaugher, B. L., Abbott, T. M., Angstadt, R., Annis, J., Antonik, M. L., Bailey, J., Ballester, O., Bernstein, J. P., Bernstein, R. A., Bonati, M., et al. (2012). Status of the dark energy survey camera (decam) project. In Ground-based and Airborne Instrumentation for Astronomy IV, volume 8446, pages 343–357. SPIE.
Freeman et al., (1991) Freeman, T., Byrd, G., and Howard, S. (1991). Simulating ngc 4622: A leading-arm spiral galaxy. In BASS, volume 23, page 1460.
Gammie et al., (2004) Gammie, C. F., Shapiro, S. L., and McKinney, J. C. (2004). Black hole spin evolution. Astrophysical Journal, 602(1):312.
Garriga et al., (2016) Garriga, J., Vilenkin, A., and Zhang, J. (2016). Black holes and the multiverse. JCAP, 2016(02):064.
(79) Gaztanaga, E. (2022a). The black hole universe, part i. Symmetry, 14(9):1849.
(80) Gaztanaga, E. (2022b). The black hole universe, part ii. Symmetry, 14(10):1984.
Ghosh et al., (2016) Ghosh, S., Jain, P., Kashyap, G., Kothari, R., Nadkarni-Ghosh, S., and Tiwari, P. (2016). Probing statistical isotropy of cosmological radio sources using square kilometre array. JOAA, 37(4):1–21.
Gödel, (1949) Gödel, K. (1949). An example of a new type of cosmological solutions of einstein’s field equations of gravitation. Reviews of Modern Physics, 21(3):447.
Gruppuso, (2007) Gruppuso, A. (2007). Complete statistical analysis for the quadrupole amplitude in an ellipsoidal universe. Physical Review D, 76(8):083010.
Gruppuso et al., (2018) Gruppuso, A., Kitazawa, N., Lattanzi, M., Mandolesi, N., Natoli, P., and Sagnotti, A. (2018). The evens and odds of cmb anomalies. Physics of the Dark Universe, 20:49–64.
Hall and Nomura, (2008) Hall, L. J. and Nomura, Y. (2008). Evidence for the multiverse in the standard model and beyond. Physical Review D, 78(3):035001.
Haug, (2022) Haug, E. G. (2022). Does lorentz relativistic mass make dark energy superfluous? Universe, 8(11):577.
Hayasaki and Loeb, (2016) Hayasaki, K. and Loeb, A. (2016). Detection of gravitational wave emission by supermassive black hole binaries through tidal disruption flares. Scientific Reports, 6(1):1–8.
Hayes et al., (2017) Hayes, W. B., Davis, D., and Silva, P. (2017). On the nature and correction of the spurious s-wise spiral galaxy winding bias in galaxy zoo 1. Monthyl Notices of the Royal Astronomical Society, 466(4):3928–3936.
Heinz and Merloni, (2004) Heinz, S. and Merloni, A. (2004). Constraints on relativistic beaming from estimators of the unbeamed flux. Monthyl Notices of the Royal Astronomical Society, 355(1):L1–L5.
Helmert, (1876) Helmert, F. (1876). Die genauigkeit der formel von peters zur berechnung des wahrscheinlichen beobachtungsfehlers director beobachtungen gleicher genauigkeit. Astronomical Notes, 88:113.
Hirata et al., (2007) Hirata, C. M., Mandelbaum, R., Ishak, M., Seljak, U., Nichol, R., Pimbblet, K. A., Ross, N. P., and Wake, D. (2007). Intrinsic galaxy alignments from the 2slaq and sdss surveys: luminosity and redshift scalings and implications for weak lensing surveys. Monthly Notices of the Royal Astronomical Society, 381(3):1197–1218.
Hoehn and Shamir, (2014) Hoehn, C. and Shamir, L. (2014). Characteristics of clockwise and counterclockwise spiral galaxies. Astronomical Notes, 335(2):188–191.
Hofmeister and Criss, (2020) Hofmeister, A. M. and Criss, R. E. (2020). Debate on the physics of galactic rotation and the existence of dark matter.
Hou et al., (2022) Hou, J., Slepian, Z., and Cahn, R. N. (2022). Measurement of parity-odd modes in the large-scale 4-point correlation function of sdss boss dr12 cmass and lowz galaxies. arXiv:2206.03625.
Hutsemekers, (1998) Hutsemekers, D. (1998). Evidence for very large-scale coherent orientations of quasar polarization vectors. Astronomy & Astrophysics, 332:410–428.
Hutsemékers et al., (2005) Hutsemékers, D., Cabanac, R., Lamy, H., and Sluse, D. (2005). Mapping extreme-scale alignments of quasar polarization vectors. Astronomy & Astrophysics, 441(3):915–930.
Iocco et al., (2015) Iocco, F., Pato, M., and Bertone, G. (2015). Testing modified newtonian dynamics in the milky way. Physical Review D, 92(8):084046.
Ishwara-Chandra and Saikia, (2000) Ishwara-Chandra, C. and Saikia, D. (2000). Relativistic beaming effects in the spectra of cores and hotspots in radio galaxies and quasars. Monthyl Notices of the Royal Astronomical Society, 317(3):658–666.
Iye and Sugai, (1991) Iye, M. and Sugai, H. (1991). A catalog of spin orientation of southern galaxies. Astrophysical Journal, 374:112–116.
Iye et al., (2021) Iye, M., Yagi, M., and Fukumoto, H. (2021). Spin parity of spiral galaxies iii–dipole analysis of the distribution of sdss spirals with 3d random walk simulation. Astrophysical Journal, 907:123.
Jaime, (2021) Jaime, L. G. (2021). On the viability of the evolution of the universe with geometric inflation. Physics of the Dark Universe, 34:100887.
Javanmardi and Kroupa, (2017) Javanmardi, B. and Kroupa, P. (2017). Anisotropy in the all-sky distribution of galaxy morphological types. Astronomy & Astrophysics, 597:A120.
Javanmardi et al., (2015) Javanmardi, B., Porciani, C., Kroupa, P., and Pflam-Altenburg, J. (2015). Probing the isotropy of cosmic acceleration traced by type ia supernovae. Astrophysical Journal, 810(1):47.
Jones et al., (2005) Jones, B. J., Martínez, V. J., Saar, E., and Trimble, V. (2005). Scaling laws in the distribution of galaxies. Reviews of Modern Physics, 76(4):1211.
Kamionkowski and Loeb, (1997) Kamionkowski, M. and Loeb, A. (1997). Getting around cosmic variance. Physical Review D, 56(8):4511.
Kavya et al., (2022) Kavya, N., Venkatesha, V., Mandal, S., and Sahoo, P. (2022). Constraining anisotropic cosmological model in f( $\mathscr{R}$ , $\mathscr{L}_{m})$ gravity. Physics of the Dark Universe, 38:101126.
Keenan et al., (2020) Keenan, R. P., Marrone, D. P., and Keating, G. K. (2020). Biases and cosmic variance in molecular gas abundance measurements at high redshift. Astrophysical Journal, 904(2):127.
Khetan et al., (2021) Khetan, N., Izzo, L., Branchesi, M., Wojtak, R., Cantiello, M., Murugeshan, C., Agnello, A., Cappellaro, E., Della Valle, M., Gall, C., Hjorth, J., Benetti, S., Brocato, E., Burke, J., Hiramatsu, D., Howell, D. A., Tomasella, L., and Valenti, S. (2021). A new measurement of the hubble constant using type ia supernovae calibrated with surface brightness fluctuations. Astronomy & Astrophysics, 647:A72.
(109) Kim, J. and Naselsky, P. (2010a). Anomalous parity asymmetry of the wilkinson microwave anisotropy probe power spectrum data at low multipoles. ApJL, 714(2):L265.
(110) Kim, J. and Naselsky, P. (2010b). Anomalous parity asymmetry of wmap 7-year power spectrum data at low multipoles: is it cosmological or systematics? Physical Review D, 82(6):063002.
Koekemoer et al., (2007) Koekemoer, A. M., Aussel, H., Calzetti, D., Capak, P., Giavalisco, M., Kneib, J.-P., Leauthaud, A., Le Fevre, O., McCracken, H., Massey, R., et al. (2007). The cosmos survey: Hubble space telescope advanced camera for surveys observations and data processing. Astrophysical Journal Supplement Series, 172(1):196.
Kragh, (2009) Kragh, H. (2009). Contemporary history of cosmology and the controversy over the multiverse. Annals of Science, 66(4):529–551.
Krishnan et al., (2021) Krishnan, C., Mohayaee, R., Colgáin, E. Ó., Sheikh-Jabbari, M., and Yin, L. (2021). Does hubble tension signal a breakdown in flrw cosmology? Classical and Quantum Gravity, 38(18):184001.
Krishnan et al., (2022) Krishnan, C., Mohayaee, R., Colgáin, E. Ó., Sheikh-Jabbari, M., and Yin, L. (2022). Hints of flrw breakdown from supernovae. Physical Review D, 105(6):063514.
Kroupa, (2012) Kroupa, P. (2012). The dark matter crisis: falsification of the current standard model of cosmology. Publications of the Astronomical Society of Australia, 29(4):395–433.
Kroupa, (2015) Kroupa, P. (2015). Galaxies as simple dynamical systems: observational data disfavor dark matter and stochastic star formation. Canadian Journal of Physics, 93(2):169–202.
Kroupa et al., (2012) Kroupa, P., Pawlowski, M., and Milgrom, M. (2012). The failures of the standard model of cosmology require a new paradigm. International Journal of Modern Physics D, 21(14):1230003.
Land and Magueijo, (2005) Land, K. and Magueijo, J. (2005). Examination of evidence for a preferred axis in the cosmic radiation anisotropy. PRL, 95(7):071301.
Land et al., (2008) Land, K., Slosar, A., Lintott, C., Andreescu, D., Bamford, S., Murray, P., Nichol, R., Raddick, M. J., Schawinski, K., Szalay, A., et al. (2008). Galaxy zoo: the large-scale spin statistics of spiral galaxies in the sloan digital sky survey. Monthyl Notices of the Royal Astronomical Society, 388(4):1686–1692.
Larin, (2022) Larin, S. A. (2022). Towards the explanation of flatness of galaxies rotation curves. Universe, 8(12):632.
(121) Lee, J., Kim, S., Jeong, H., Smith, R., Choi, H., Hwang, H. S., Joo, S.-J., Kim, H.-S., Lee, Y., and Sukyoung, K. Y. (2018a). Wobbling galaxy spin axes in dense environments. Astrophysical Journal, 864(1):69.
(122) Lee, J. C., Hwang, H. S., and Chung, H. (2018b). A study of environmental effects on galaxy spin using manga data. Monthly Notices of the Royal Astronomical Society, 477(2):1567–1577.
(123) Lee, J. H., Pak, M., Lee, H.-R., and Song, H. (2019a). Galaxy rotation coherent with the motions of neighbors: Discovery of observational evidence. Astrophysical Journal, 872(1):78.
(124) Lee, J. H., Pak, M., Song, H., Lee, H.-R., Kim, S., and Jeong, H. (2019b). Mysterious coherence in several-megaparsec scales between galaxy rotation and neighbor motion. Astrophysical Journal, 884(2):104.
Libeskind et al., (2013) Libeskind, N. I., Hoffman, Y., Forero-Romero, J., Gottlöber, S., Knebe, A., Steinmetz, M., and Klypin, A. (2013). The velocity shear tensor: tracer of halo alignment. Monthyl Notices of the Royal Astronomical Society, 428(3):2489–2499.
Lin et al., (2016) Lin, H.-N., Li, X., and Chang, Z. (2016). The significance of anisotropic signals hiding in the type ia supernovae. Monthyl Notices of the Royal Astronomical Society, 460(1):617–626.
Lintott et al., (2008) Lintott, C. J., Schawinski, K., Slosar, A., Land, K., Bamford, S., Thomas, D., Raddick, M. J., Nichol, R. C., Szalay, A., Andreescu, D., et al. (2008). Galaxy zoo: morphologies derived from visual inspection of galaxies from the sloan digital sky survey. Monthly Notices of the Royal Astronomical Society, 389(3):1179–1189.
Lister, (2001) Lister, M. L. (2001). Relativistic beaming and flux variability in active galactic nuclei. Astrophysical Journal, 561(2):676.
Loeb and Gaudi, (2003) Loeb, A. and Gaudi, B. S. (2003). Periodic flux variability of stars due to the reflex doppler effect induced by planetary companions. Astrophysical Journal Letters, 588(2):L117.
Longo, (2011) Longo, M. J. (2011). Detection of a dipole in the handedness of spiral galaxies with redshifts z 0.04. Physics Letters B, 699(4):224–229.
Luongo et al., (2022) Luongo, O., Muccino, M., Colgáin, E. Ó., Sheikh-Jabbari, M., and Yin, L. (2022). Larger $h_{0}$ values in the cmb dipole direction. Physical Review D, 105(10):103510.
MacGillivray and Dodd, (1985) MacGillivray, H. and Dodd, R. (1985). The anisotropy of the spatial orientations of galaxies in the local supercluster. Astronomy & Astrophysics, 145:269–274.
Mackenzie et al., (2017) Mackenzie, R., Shanks, T., Bremer, M. N., Cai, Y.-C., Gunawardhana, M. L., Kovács, A., Norberg, P., and Szapudi, I. (2017). Evidence against a supervoid causing the cmb cold spot. Monthyl Notices of the Royal Astronomical Society, 470(2):2328–2338.
Mandelbaum et al., (2006) Mandelbaum, R., Seljak, U., Kauffmann, G., Hirata, C. M., and Brinkmann, J. (2006). Galaxy halo masses and satellite fractions from galaxy–galaxy lensing in the sloan digital sky survey: stellar mass, luminosity, morphology and environment dependencies. Monthly Notices of the Royal Astronomical Society, 368(2):715–731.
Mannheim, (2006) Mannheim, P. D. (2006). Alternatives to dark matter and dark energy. Progress in Particle and Nuclear Physics, 56(2):340–445.
Marcha and Browne, (2021) Marcha, M. J. M. and Browne, I. W. A. (2021). Large-scale clustering amongst Fermi blazars; evidence for axis alignments? Monthly Notices of the Royal Astronomical Society, 507(1):1361–1368.
Mariano and Perivolaropoulos, (2013) Mariano, A. and Perivolaropoulos, L. (2013). Cmb maximum temperature asymmetry axis: Alignment with other cosmic asymmetries. Physical Review D, 87(4):043511.
Masina and Notari, (2009) Masina, I. and Notari, A. (2009). The cold spot as a large void: lensing effect on cmb two and three point correlation functions. JCAP, 2009(07):035.
Mayall, (1951) Mayall, N. (1951). In the structure of the galaxy. 19. Ann Arbor: Univ. Mich. Press.
McClintock et al., (2006) McClintock, J. E., Shafee, R., Narayan, R., Remillard, R. A., Davis, S. W., and Li, L.-X. (2006). The spin of the near-extreme kerr black hole grs 1915+ 105. Astrophysical Journal, 652(1):518.
Meldorf et al., (2022) Meldorf, C., Palmese, A., Brout, D., Chen, R., Scolnic, D., Kelsey, L., Galbany, L., Hartley, W. G., Davis, T. M., Drlica-Wagner, A., Vincenzi, M., Annis, J., Dixon, M., Graur, O., Lidman, C., Möller, A., Nugent, P., Rose, B., Smith, M., Allam, S., Tucker, D. L., Asorey, J., Calcino, J., Carollo, D., Glazebrook, K., Lewis, G. F., Taylor, G., Tucker, B. E., Kim, A. G., Diehl, H. T., Aguena, M., Andrade-Oliveira, F., Bacon, D., Bertin, E., Bocquet, S., Brooks, D., Burke, D. L., Carretero, J., Kind, M. C., Castander, F. J., Costanzi, M., da Costa, L. N., Desai, S., Doel, P., Everett, S., Ferrero, I., Friedel, D., Frieman, J., García-Bellido, J., Gatti, M., Gruen, D., Gschwend, J., Gutierrez, G., Hinton, S. R., Hollowood, D. L., Honscheid, K., James, D. J., Kuehn, K., March, M., Marshall, J. L., Menanteau, F., Miquel, R., Morgan, R., Paz-Chinchón, F., Pereira, M. E. S., Malagón, A. A. P., Sanchez, E., Scarpine, V., Sevilla-Noarbe, I., Suchyta, E., Tarle, G., Varga, T. N., and DES, C. (2022). The dark energy survey supernova program results: Type ia supernova brightness correlates with host galaxy dust. Monthly Notices of the Royal Astronomical Society. stac3056.
Mészáros, (2019) Mészáros, A. (2019). An oppositeness in the cosmology: Distribution of the gamma ray bursts and the cosmological principle. Astronomical Notes, 340(7):564–569.
Migkas et al., (2021) Migkas, K., Pacaud, F., Schellenberger, G., Erler, J., Nguyen-Dang, N., Reiprich, T., Ramos-Ceja, M., and Lovisari, L. (2021). Cosmological implications of the anisotropy of ten galaxy cluster scaling relations. Astronomy & Astrophysics, 649:A151.
Migkas et al., (2020) Migkas, K., Schellenberger, G., Reiprich, T., Pacaud, F., Ramos-Ceja, M., and Lovisari, L. (2020). Probing cosmic isotropy with a new x-ray galaxy cluster sample through the lx–t scaling relation. Astronomy & Astrophysics, 636:A15.
Milgrom, (1983) Milgrom, M. (1983). A modification of the newtonian dynamics as a possible alternative to the hidden mass hypothesis. Astrophysical Journal, 270:365–370.
Milgrom, (2007) Milgrom, M. (2007). Mond and the mass discrepancies in tidal dwarf galaxies. Astrophysical Journal Letters, 667(1):L45.
Milgrom, (2019) Milgrom, M. (2019). Mond in galaxy groups: A superior sample. Physical Review D, 99(4):044041.
Montero et al., (2012) Montero, P. J., Janka, H.-T., and Müller, E. (2012). Relativistic collapse and explosion of rotating supermassive stars with thermonuclear effects. Astrophysical Journal, 749(1):37.
Morháč et al., (2000) Morháč, M., Kliman, J., Matoušek, V., Veselskỳ, M., and Turzo, I. (2000). Identification of peaks in multidimensional coincidence $\gamma$ -ray spectra. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 443(1):108–125.
Mörtsell and Dhawan, (2018) Mörtsell, E. and Dhawan, S. (2018). Does the hubble constant tension call for new physics? Journal of Cosmology and Astroparticle Physics, 2018(09):025.
Moster et al., (2011) Moster, B. P., Somerville, R. S., Newman, J. A., and Rix, H.-W. (2011). A cosmic variance cookbook. Astrophysical Journal, 731(2):113.
Mudambi et al., (2020) Mudambi, S. P., Rao, A., Gudennavar, S., Misra, R., and Bubbly, S. (2020). Estimation of the black hole spin in lmc x-1 using astrosat. Monthly Notices of the Royal Astronomical Society, 498(3):4404–4410.
Nagao, (2020) Nagao, S. (2020). Galactic evolution showing a constant circulating speed of stars in a galactic disc without requiring dark matter. Reports in Advances of Physical Sciences, 4(02):2050004.
O’Brien et al., (2017) O’Brien, J. G., Chiarelli, T. L., Dentico, J., Stulge, M., Stefanski, B., Moss, R., and Chaykov, S. (2017). Alternative gravity rotation curves for the little things survey. Astrophysical Journal, 852(1):6.
Odo et al., (2017) Odo, F., Chukwude, A., and Ubachukwu, A. (2017). Relativistic beaming effects in bl lacertae objects: Evidence for rbl/xbl dichotomy. Astrophysics & Space Science, 362(2):23.
Oort, (1940) Oort, J. H. (1940). Some problems concerning the structure and dynamics of the galactic system and the elliptical nebulae ngc 3115 and 4494. Astrophysical Journal, 91:273.
Opik, (1922) Opik, E. (1922). An estimate of the distance of the andromeda nebula. Astrophysical Journal, 55.
Orr and Browne, (1982) Orr, M. and Browne, I. (1982). Relativistic beaming and quasar statistics. Monthyl Notices of the Royal Astronomical Society, 200(4):1067–1080.
Ozsváth and Schücking, (1962) Ozsváth, I. and Schücking, E. (1962). Finite rotating universe. Nature, 193(4821):1168–1169.
Ozsvath and Schücking, (2001) Ozsvath, I. and Schücking, E. (2001). Approaches to gödel’s rotating universe. Classical and Quantum Gravity, 18(12):2243.
Padovani and Urry, (1992) Padovani, P. and Urry, C. (1992). Luminosity functions, relativistic beaming, and unified theories of high-luminosity radio sources. Astrophysical Journal, 387:449–457.
Pandey et al., (2020) Pandey, S., Raveri, M., and Jain, B. (2020). Model independent comparison of supernova and strong lensing cosmography: Implications for the hubble constant tension. Physical Review D, 102(2):023505.
Pathria, (1972) Pathria, R. (1972). The universe as a black hole. Nature, 240(5379):298–299.
Pease, (1918) Pease, F. (1918). The rotation and radial velocity of the central part of the andromeda nebula. PNAS, 4(1):21.
Pecker, (1997) Pecker, J.-C. (1997). Some critiques of the big bang cosmology. JOAA, 18(4):323–333.
Perivolaropoulos, (2014) Perivolaropoulos, L. (2014). Large scale cosmological anomalies and inhomogeneous dark energy. Galaxies, 2(1):22–61.
Philcox, (2022) Philcox, O. H. (2022). Probing parity-violation with the four-point correlation function of boss galaxies. arXiv:2206.04227.
Piao, (2005) Piao, Y.-S. (2005). Possible explanation to a low cmb quadrupole. Physical Review D, 71(8):087301.
Piao et al., (2004) Piao, Y.-S., Feng, B., and Zhang, X. (2004). Suppressing the cmb quadrupole with a bounce from the contracting phase to inflation. Physical Review D, 69(10):103520.
Popławski, (2010) Popławski, N. J. (2010). Radial motion into an einstein–rosen bridge. PLB, 687(2-3):110–113.
Popławski, (2021) Popławski, N. J. (2021). A nonsingular, anisotropic universe in a black hole with torsion and particle production. General Relativity and Gravitation, 53(2):1–14.
Rajpoot and Vacaru, (2017) Rajpoot, S. and Vacaru, S. I. (2017). On supersymmetric geometric flows and r2 inflation from scale invariant supergravity. Annals of Physics, 384:20–60.
Ralston and Jain, (2004) Ralston, J. P. and Jain, P. (2004). The virgo alignment puzzle in propagation of radiation on cosmological scales. International Journal of Modern Physics D, 13(09):1857–1877.
Reynolds, (2013) Reynolds, C. S. (2013). Black holes in a spin. Nature, 494(7438):432–433.
Reynolds, (2019) Reynolds, C. S. (2019). Observing black holes spin. Nature Astronomy, 3(1):41–47.
Reynolds, (2021) Reynolds, C. S. (2021). Observational constraints on black hole spin. Annual Review of Astronomy and Astrophysics, 59:117–154.
Riess et al., (2019) Riess, A. G., Casertano, S., Yuan, W., Macri, L. M., and Scolnic, D. (2019). Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond $\lambda$ cdm. Astrophysical Journal, 876(1):85.
Riess et al., (2022) Riess, A. G., Yuan, W., Macri, L. M., Scolnic, D., Brout, D., Casertano, S., Jones, D. O., Murakami, Y., Anand, G. S., Breuval, L., et al. (2022). A comprehensive measurement of the local value of the hubble constant with 1 km s- 1 mpc- 1 uncertainty from the hubble space telescope and the sh0es team. Astrophysical Journal Letters, 934(1):L7.
Rivera, (2020) Rivera, P. C. (2020). An alternative model of rotation curve that explains anomalous orbital velocity, mass discrepancy and structure of some galaxies. American Journal of Astronomy and Astrophysics, 7(4):73–79.
Rodrigues, (2008) Rodrigues, D. C. (2008). Anisotropic cosmological constant and the cmb quadrupole anomaly. Physical Review D, 77(2):023534.
Rubin, (1983) Rubin, V. C. (1983). The rotation of spiral galaxies. Science, 220(4604):1339–1344.
Rubin, (2000) Rubin, V. C. (2000). One hundred years of rotating galaxies. Publications of the Astronomical Society of the Pacific, 112(772):747.
Rubin et al., (1985) Rubin, V. C., Burstein, D., Ford Jr, W. K., and Thonnard, N. (1985). Rotation velocities of 16 sa galaxies and a comparison of sa, sb, and sc rotation properties. Astrophysical Journal, 289:81–98.
Rubin and Ford Jr, (1970) Rubin, V. C. and Ford Jr, W. K. (1970). Rotation of the andromeda nebula from a spectroscopic survey of emission regions. Astrophysical Journal, 159:379.
Rubin et al., (1978) Rubin, V. C., Ford Jr, W. K., and Thonnard, N. (1978). Extended rotation curves of high-luminosity spiral galaxies. iv-systematic dynamical properties, sa through sc. Astrophysical Journal, 225:L107–L111.
Rubin et al., (1980) Rubin, V. C., Ford Jr, W. K., and Thonnard, N. (1980). Rotational properties of 21 sc galaxies with a large range of luminosities and radii, from ngc 4605/r= 4kpc/to ugc 2885/r= 122 kpc. Astrophysical Journal, 238:471–487.
Rummel and Burgess, (2020) Rummel, M. and Burgess, C. (2020). Constraining fundamental physics with the event horizon telescope. Journal of Cosmology and Astropracticle Physics, 2020(05):051.
Rybicki and Lightman, (2008) Rybicki, G. B. and Lightman, A. P. (2008). Radiative processes in astrophysics. John Wiley & Sons.
Sanders, (1990) Sanders, R. (1990). Mass discrepancies in galaxies: dark matter and alternatives. The Astronomy and Astrophysics Review, 2(1):1–28.
Sanders, (1998) Sanders, R. (1998). The virial discrepancy in clusters of galaxies in the context of modified newtonian dynamics. ApJL, 512(1):L23.
Sanders, (2012) Sanders, R. (2012). Ngc 2419 does not challenge modified newtonian dynamics. Monthly Notices of the Royal Astronomical Society, 419(1):L6–L8.
Sanders and McGaugh, (2002) Sanders, R. H. and McGaugh, S. S. (2002). Modified newtonian dynamics as an alternative to dark matter. Annual Review of Astronomy and Astrophysics, 40(1):263–317.
Santos et al., (2015) Santos, L., Cabella, P., Villela, T., and Zhao, W. (2015). Influence of planck foreground masks in the large angular scale quadrant cmb asymmetry. Astronomy & Astrophysics, 584:A115.
Savolainen et al., (2010) Savolainen, T., Homan, D., Hovatta, T., Kadler, M., Kovalev, Y., Lister, M., Ros, E., and Zensus, J. (2010). Relativistic beaming and gamma-ray brightness of blazars. Astronomy & Astrophysics, 512:A24.
Schwarz et al., (2004) Schwarz, D. J., Starkman, G. D., Huterer, D., and Copi, C. J. (2004). Is the low-l microwave background cosmic? PRL, 93(22):221301.
Schwarzschild, (1954) Schwarzschild, M. (1954). Mass distribution and mass-luminosity ratio in galaxies. Astronomical Journal, 59:273.
Scoville et al., (2007) Scoville, N., Abraham, R., Aussel, H., Barnes, J., Benson, A., Blain, A., Calzetti, D., Comastri, A., Capak, P., Carilli, C., et al. (2007). Cosmos: Hubble space telescope observations. Astrophysical Journal Supplement Series, 172(1):38.
Secrest et al., (2021) Secrest, N. J., von Hausegger, S., Rameez, M., Mohayaee, R., Sarkar, S., and Colin, J. (2021). A test of the cosmological principle with quasars. ApJL, 908(2):L51.
Semenaite et al., (2021) Semenaite, A., Sánchez, A. G., Pezzotta, A., Hou, J., Scoccimarro, R., Eggemeier, A., Crocce, M., Chuang, C.-H., Smith, A., Zhao, C., et al. (2021). Cosmological implications of the full shape of anisotropic clustering measurements in boss and eboss. Monthly Notices of the Royal Astronomical Society, 512(4):5657–5670.
Seshavatharam, (2010) Seshavatharam, U. (2010). Physics of rotating and expanding black hole universe. Progress in Physics, 2:7–14.
Seshavatharam and Lakshminarayana, (2020) Seshavatharam, U. and Lakshminarayana, S. (2020). An integrated model of a light speed rotating universe. International Astronomy and Astrophysics Research Journal, pages 74–82.
Seshavatharam and Lakshminarayana, (2022) Seshavatharam, U. V. S. and Lakshminarayana, S. (2022). Concepts and results of a practical model of quantum cosmology: Light speed expanding black hole cosmology. Mapana Journal of Sciences, 21(2).
Shamir, (2011) Shamir, L. (2011). Ganalyzer: A tool for automatic galaxy image analysis. Astrophysical Journal, 736(2):141.
Shamir, (2012) Shamir, L. (2012). Handedness asymmetry of spiral galaxies with z¡ 0.3 shows cosmic parity violation and a dipole axis. Physics Letters B, 715(1):25–29.
Shamir, (2013) Shamir, L. (2013). Color differences between clockwise and counterclockwise spiral galaxies. Galaxies, 1(3):210–215.
Shamir, (2016) Shamir, L. (2016). Asymmetry between galaxies with clockwise handedness and counterclockwise handedness. Astrophysical Journal, 823(1):32.
(207) Shamir, L. (2017a). Colour asymmetry between galaxies with clockwise and counterclockwise handedness. Astrophysics & Space Science, 362(2):33.
(208) Shamir, L. (2017b). Large-scale photometric asymmetry in galaxy spin patterns. Publications of the Astronomical Society of Australia, 34:e44.
(209) Shamir, L. (2017c). Photometric asymmetry between clockwise and counterclockwise spiral galaxies in sdss. Publications of the Astronomical Society of Australia, 34:e011.
(210) Shamir, L. (2019a). Cosmological-scale parity violation of galaxy spin patterns. arXiv preprint arXiv:1912.05429.
(211) Shamir, L. (2019b). Large-scale patterns of galaxy spin rotation show cosmological-scale parity violation and multipoles. arXiv, page 1912.05429.
(212) Shamir, L. (2020a). Asymmetry between galaxies with different spin patterns: A comparison between cosmos, sdss, and pan-starrs. Open Astronomy, 29(1):15–27.
(213) Shamir, L. (2020b). Galaxy spin direction distribution in hst and sdss show similar large-scale asymmetry. Publications of the Astronomical Society of Australia, 37:e053.
(214) Shamir, L. (2020c). Patterns of galaxy spin directions in sdss and pan-starrs show parity violation and multipoles. Astrophysics & Space Science, 365:136.
(215) Shamir, L. (2021a). Analysis of the alignment of non-random patterns of spin directions in populations of spiral galaxies. Particles, 4(1):11–28.
(216) Shamir, L. (2021b). Large-scale asymmetry in galaxy spin directions: evidence from the southern hemisphere. Publications of the Astronomical Society of Australia, 38:e037.
(217) Shamir, L. (2022a). Analysis of $\sim 10^{6}$ spiral galaxies from four telescopes shows large-scale patterns of asymmetry in galaxy spin directions. Advances in Astronomy, 2022:8462363.
(218) Shamir, L. (2022b). Analysis of spin directions of galaxies in the desi legacy survey. Monthly Notices of the Royal Astronomical Society, 516(2):2281–2291.
(219) Shamir, L. (2022c). Asymmetry in galaxy spin directions - analysis of data from des and comparison to four other sky surveys. Universe, 8:8.
(220) Shamir, L. (2022d). Large-scale asymmetry in galaxy spin directions: analysis of galaxies with spectra in des, sdss, and desi legacy survey. Astronomical Notes, 343(6-7):e20220010.
(221) Shamir, L. (2022e). A possible large-scale alignment of galaxy spin directions - analysis of 10 datasets from sdss, pan-starrs, and hst. New Astronomy, 95:101819.
(222) Shamir, L. (2022f). Using 3d and 2d analysis for analyzing large-scale asymmetry in galaxy spin directions. PASJ, 74(5):1114–1130.
(223) Shamir, L. (2022g). Using machine learning to profile asymmetry between spiral galaxies with opposite spin directions. Symmetry, 14(5).
Singal, (2019) Singal, A. K. (2019). Large disparity in cosmic reference frames determined from the sky distributions of radio sources and the microwave background radiation. Physical Review D, 100(6):063501.
Sivaram and Arun, (2012) Sivaram, C. and Arun, K. (2012). Primordial rotation of the universe, hydrodynamics, vortices and angular momenta of celestial objects. Open Astronomy, 5:7–11.
Sivaram et al., (2020) Sivaram, C., Arun, K., and Rebecca, L. (2020). Mond, mong, morg as alternatives to dark matter and dark energy, and consequences for cosmic structures. Journal of Astrophysics and Astronomy, 41(1):1–6.
Skeivalas et al., (2021) Skeivalas, J., Paršeliūnas, E., and Šlikas, D. (2021). The predictive model for the universe rotation axis identification upon applying the solar system coordinate net in the milky way galaxy. Indian Journal of Physics, pages 1–10.
Skordis and Złośnik, (2019) Skordis, C. and Złośnik, T. (2019). Gravitational alternatives to dark matter with tensor mode speed equaling the speed of light. Physical Review D, 100(10):104013.
Slipher, (1914) Slipher, V. M. (1914). The detection of nebular rotation. Lowell Observatory Bulletin, 2:66–66.
Sofue and Rubin, (2001) Sofue, Y. and Rubin, V. (2001). Rotation curves of spiral galaxies. Annual Review of Astronomy and Astrophysics, 39:137–174.
Sommers, (2001) Sommers, P. (2001). Cosmic ray anisotropy analysis with a full-sky observatory. Astroparticle Physics, 14(4):271–286.
Stuckey, (1994) Stuckey, W. (1994). The observable universe inside a black hole. American Journal of Physics, 62(9):788–795.
Su and Chu, (2009) Su, S.-C. and Chu, M.-C. (2009). Is the universe rotating? Astrophysical Journal, 703(1):354.
Swaters et al., (2010) Swaters, R., Sanders, R., and McGaugh, S. (2010). Testing modified newtonian dynamics with rotation curves of dwarf and low surface brightness galaxies. Astrophysical Journal, 718(1):380.
Takahashi, (2004) Takahashi, R. (2004). Shapes and positions of black hole shadows in accretion disks and spin parameters of black holes. Astrophysical Journal, 611(2):996.
Tatum et al., (2018) Tatum, E. T., Seshavatharam, U., et al. (2018). Clues to the fundamental nature of gravity, dark energy and dark matter. Journal of Modern Physics, 9(08):1469.
(237) Tatum, E. T., Seshavatharam, U., Lakshminarayana, S., et al. (2015a). The basics of flat space cosmology. International journal of Astronomy and Astrophysics, 5(02):116.
(238) Tatum, E. T., Seshavatharam, U., Lakshminarayana, S., et al. (2015b). Flat space cosmology as a mathematical model of quantum gravity or quantum cosmology. International journal of astronomy and astrophysics, 5(03):133.
Tiwari and Jain, (2015) Tiwari, P. and Jain, P. (2015). Dipole anisotropy in integrated linearly polarized flux density in nvss data. Monthly Notices of the Royal Astronomical Society, 447(3):2658–2670.
Tiwari and Nusser, (2016) Tiwari, P. and Nusser, A. (2016). Revisiting the nvss number count dipole. JCAP, 2016(03):062.
Trimble, (2009) Trimble, V. (2009). Multiverses of the past. Astronomical Notes, 330(7):761–769.
Van Waerbeke et al., (2000) Van Waerbeke, L., Mellier, Y., Erben, T., Cuillandre, J., Bernardeau, F., Maoli, R., Bertin, E., Mc Cracken, H., Fevre, O. L., Fort, B., et al. (2000). Detection of correlated galaxy ellipticities on cfht data: first evidence for gravitational lensing by large-scale structures. Astronomy and Astrophysics, 358:30–44.
Velten and Gomes, (2020) Velten, H. and Gomes, S. (2020). Is the hubble diagram of quasars in tension with concordance cosmology? Physical Review D, 101(4):043502.
Vielva, (2010) Vielva, P. (2010). A comprehensive overview of the cold spot. Advances in Astronomy, 2010.
Volonteri et al., (2005) Volonteri, M., Madau, P., Quataert, E., and Rees, M. J. (2005). The distribution and cosmic evolution of massive black hole spins. Astrophysical Journal, 620(1):69.
Webb et al., (2011) Webb, J., King, J., Murphy, M., Flambaum, V., Carswell, R., and Bainbridge, M. (2011). Indications of a spatial variation of the fine structure constant. PRL, 107(19):191101.
Wills and Browne, (1986) Wills, B. J. and Browne, I. (1986). Relativistic beaming and quasar emission lines. Astrophysical Journal, 302:56–63.
Wittman et al., (2000) Wittman, D. M., Tyson, J. A., Kirkman, D., Dell’Antonio, I., and Bernstein, G. (2000). Detection of weak gravitational lensing distortions of distant galaxies by cosmic dark matter at large scales. Nature, 405(6783):143–148.
Wojnar et al., (2018) Wojnar, A., Sporea, C., and Borowiec, A. (2018). A simple model for explaining galaxy rotation curves. Galaxies, 6(3):70.
Wolf, (1914) Wolf, M. (1914). Vierteljahresschr astron. Ges, 49:162.
Wu and Huterer, (2017) Wu, H.-Y. and Huterer, D. (2017). Sample variance in the local measurements of the hubble constant. Monthly Notices of the Royal Astronomical Society, 471(4):4946–4955.
Yeung and Chu, (2022) Yeung, S. and Chu, M.-C. (2022). Directional variations of cosmological parameters from the planck cmb data. Physical Review D, 105(8):083508.
Zhao and Xia, (2021) Zhao, D. and Xia, J.-Q. (2021). A tomographic test of cosmic anisotropy with the recently-released quasar sample. The European Physical Journal C, 81(10):1–11.
Zhou et al., (2020) Zhou, Y., Del Popolo, A., and Chang, Z. (2020). On the absence of a universal surface density, and a maximum newtonian acceleration in dark matter haloes: Consequences for mond. Physics of the Dark Universe, 28:100468.
Zwicky, (1937) Zwicky, F. (1937). On the masses of nebulae and of clusters of nebulae. Astrophysical Journal, 86:217.