JWST high redshift galaxy observations have a strong tension with Planck CMB measurements

Since the cosmic acceleration is discovered by Type Ia supernovae (SNe Ia) SupernovaSearchTeam:1998fmf ; SupernovaCosmologyProject:1998vns and confirmed by two independent probes cosmic microwave background (CMB) WMAP:2003elm ; Planck:2013pxb ; Planck:2018vyg and baryon acoustic oscillations (BAO) Blake:2003rh ; Seo:2003 , the standard 6-parameter cosmological model, $\Lambda$-cold dark matter ($\Lambda$CDM) has achieved great success in characterizing the physical phenomena across multiple scales at the background and perturbation levels. However, the validity of $\Lambda$CDM is challenged by various kinds of new observations for a long time, and consequently new puzzles emerge such as the so-called Hubble constant ($H_{0}$) tension (see DiValentino:2020vhf ; Abdalla:2022yfr for recent reviews). It is noteworthy that, so far, we can not study effectively the correctness of $\Lambda$CDM around redshift $z\sim 10$, since currently mainstream probes BAO and SNe Ia can not give direct observations at high redshifts. The lack of stable high redshift observations will prevent us from testing $\Lambda$CDM more completely during the early stage of the evolution of our universe.

Very excitingly, the recent released high redshift galaxy observations Labbe:2022 ; Harikane:2022 ; Naidu:2022 ; Castellano:2022 in the range $z\in[7,11]$ by JWST, which contains a population of surprisingly massive galaxy candidates with stellar masses of order of $10^{9}M_{\odot}$, can help explore whether $\Lambda$CDM is valid at high redshifts. In the literature, Refs.Labbe:2022 ; Harikane:2022 ; Boylan-Kolchin:2022kae ; Lovell:2022bhx have reported the cumulative stellar mass density (CSMD) estimated from early JWST data is higher than that predicted by $\Lambda$CDM within $z\in[7,11]$. Ref.Menci:2022wia points out that dynamical dark energy (DDE) can explain this anomalous signal and the corresponding constraint on DDE is displayed. Subsequently, if the nature of dark matter (DM) is fuzzy, this high SMD can be recovered Gong:2022qjx . Furthermore, Ref.Biagetti:2022ode discusses under which circumstances primordial non-Gaussianity can act as a solution.

Since these high redshift galaxy observations from JWST have important implications on cosmology and astrophysics, we attempt to probe whether early JWST data indicates any possible signal of new physics. Specifically, we study three classes of beyond $\Lambda$CDM cosmological models, i.e., DM-baryon interaction (DMBI), modified gravity (MG) and DDE. In addition, we consider the case of the extended halo mass function (HMF). We find that Within current cosmological constraints from Planck-2018 CMB obervations, these three models all fail to explain this large tension. A possibly successful scenario to escape from cosmological constraints is the extended Press-Schechter formalism.

This study is outlined in the following manner. In the next section, we introduce the basic formula of CSMD. In Section III, we review briefly the alternative cosmological models and extended Press-Schechter HMF. In Section IV, numerical results are displayed. The discussions and conclusions are presented in the final section.

As shown in Ref.Labbe:2022 , the CSMD from early JWST data has a large excess relative to that predicted by $\Lambda$CDM. To explain this excess, we shall briefly introduce the basic formula of the cumulative SMD. The HMF for a given cosmological model reads as

$$\frac{{\rm d}n}{{\rm d}M}=F(\nu)\frac{\rho_{m}}{M^{2}}\left|\frac{{\rm d}\ln\sigma}{{\rm d}\ln M}\right|,$$

(1)

where the function $F(\nu)$ for the Press-Schechter HMF Press:1973iz is expressed as

$$F(\nu)=\sqrt{\frac{2}{\pi}}\nu\mathrm{e}^{-\frac{\nu^{2}}{2}},$$

(2)

and $\rho_{m}$ denotes the average background matter density, $M$ the halo mass, $\sigma$ the variance of smoothed linear matter density field and reads as

$$\sigma^{2}(R)=\frac{1}{2\pi^{2}}\int_{0}^{\infty}k^{2}P(k)W^{2}(kR){\rm dk},$$

(3)

where $k$ is the comoving wavenumber, $P(k)$ the matter power spectrum, $W(kR)=3(\sin kR-kR\cos kR)/(kR)^{3}$ the Fourier transformation of a spherical top-hat filter with radius $R=[3M/(4\pi\bar{\rho}_{0})]^{1/3}$, $\nu=\delta_{c}/[D(z)\,\sigma]$ Carroll:1991mt ($\delta_{c}=1.686$ is the critical collapsed density) and $D(z)=g(z)/[g(0)(1+z)]$ the linear growth factor for a specific cosmological model, where $g(z)$ for $\Lambda$CDM reads as

$$g(z)=\frac{5}{2}\Omega_{m}(z)\left\{\Omega_{m}(z)^{\frac{4}{7}}-\Omega_{\Lambda}(z)+\left[1+\frac{\Omega_{m}(z)}{2}\right]\left[1+\frac{\Omega_{\Lambda}(z)}{70}\right]\right\}^{-1},$$

(4)

where $\Omega_{m}(z)$ and $\Omega_{\Lambda}(z)$ are energy densities of matter and dark energy (DE) at a given redshift, respectively.

An effective quantity to study the validity of the $\Lambda$CDM model is the CSMD $\rho_{\star}$, which can be characterized by a fraction of baryon mass contained within a given DM halo above a certain mass scale $M_{\star}$ and reads as

$$\rho_{\star}(>M_{\star},z)=\epsilon f_{b}\int_{z_{1}}^{z_{2}}\int_{\frac{M_{\star}}{\epsilon f_{b}}}^{\infty}\frac{{\rm d}n}{{\rm d}M}M{\rm d}M\frac{{\rm d}V}{{\rm d}z}\frac{{\rm d}z}{V(z_{1},z_{2})},$$

(5)

where $\epsilon$ is the star formation efficiency, $f_{b}$ the baryon fraction and $V(z_{1},z_{2})$ the comoving volume in the redshift range $z\in[z_{1},\,z_{2}]$.

At first, we employ the best fits from current cosmological constraints as our baseline values for four models. Since we hope that the following calculations can be permitted by present-day observations, our discussions and results will mainly focus on the allowed parameter space. Then, for different models, we use different Boltzmann codes to calculate their background evolution, growth factors and matter power spectrum at different redshifts. Specifically, we take CLASS Dvorkin:2013cea ; Slatyer:2018aqg ; Xu:2018efh for DMBI and use modified CAMB Lewis:1999bs ; Lewis:2013hha for $f(R)$ gravity, DDE and EPS scenarios. Note that $\Lambda$CDM is adopted in the EPS scenario. Subsequently, we compute the HMF at different redshifts for the above four models. Finally, we work out the maximal CSMD for each model according to the permitted parameter space, and check whether these scenarios are consistent with the latest JWST data. Notice that Eq.(4) is only used in the EPS model and the growth factors of the other three models are obtained from the corresponding software package.

Our numerical analysis results are presented in Figs.1-3. At first, we display the CSMD of $\Lambda$CDM in the redshift range $z\in[7,9]$ and see its performance. In general, the SFE $\epsilon$ is about $10\%$ according to current observational constraints Harikane:2022 . Nonetheless, one can see that in the top left panel of Fig.1, $10\%$ is nowhere near enough to reach the lower bounds of JWST data points in $\Lambda$CDM. One needs the star formation rate in galaxies to be at least $50\%$ in order to explain the inconsistency. In the meanwhile, one can easily find that $\epsilon=0.8$ can successfully explain two data points but $100\%$ SFE can not. Except for $\Lambda$CDM, we all calculate the maximal CSMD in the other models, i.e., assuming $\epsilon=1$.

In the second place, we make a trial to explore whether alternative cosmological models can alleviate even solve the tension between JWST and Planck CMB observations. In the DMBI case, we attempt to acquire a higher baryon fraction by the coupling between DM and baryons, and consequently explain this discrepancy occurred in $\Lambda$CDM. However, we find that varying coupling strength $\sigma_{\rm DM-b}$ hardly affects the CSMD, and only the variation of interaction DM fraction $\Omega_{\rm idm}$ affects significantly the CSMD. When assuming the DM particle mass $m_{\rm DM}=100$ GeV, the cross section $\sigma_{\rm DM-b}=10^{-42}\,\mathrm{cm}^{2}$ and choosing the fraction $\Omega_{\rm idm}=0.01$, 0.03 and 0.05, this tension can be efficiently relieved but it seems that this model is difficult to explain both data points. However, if considering the current cosmological constraint that gives a very small $\Omega_{\rm idm}$ Becker:2020hzj , DMBI still behaves like $\Lambda$CDM and can not resolve this discrepancy. We have also studied the impacts of $m_{\rm DM}$ and find different DM particle masses also can not explain JWST data.

In $f(R)$ gravity, we find small $f_{R0}$ such as 0.1 and 1 can not expalin the anomaly but a very large value $f_{R0}=10$ can do. This implies that one needs a large deviation from GR to be responsible for JWST data. Unfortunately, the latest cosmological constraint gives $\log_{10}f_{R0}<-6.32$ at the $2\,\sigma$ confidence level Wang:2022xdw , which is much smaller than 10. Therefore, similar to DMBI, $f(R)$ gravity also fails to alleviate this tension. Interestingly, this gives us a hint that, if two galaxies observed by JWST are located in the low density region of the universe where MG effect is very large, the data can be appropriately explained.

Furthermore, we are interested in whether the nature an simple extension to $\Lambda$CDM, DDE, can explain the inconsistency. As mentioned above, Ref.Menci:2022wia claimed that JWST data can clearly constrain DDE. However, within current constraining precision, we query this conclusion. To ensure the validity of our conclusion, we constrain $\Lambda$CDM and DDE models using the Planck-2018 CMB temperature and polarization data (see Fig.2), and then obtain the best fitting values of parameters of these two models. One can easily find the constrained values of model parameters of $\Lambda$CDM in Ref.Planck:2018vyg . For DDE, we obtain current baryon and CDM densities $\Omega_{b}h^{2}=0.0225$ and $\Omega_{c}h^{2}=0.1184$, the ratio between angular diameter distance and sound horizon at the redshift of last scattering $\theta_{MC}=1.04109$, the optical depth due to the reionization $\tau=0.06$, the amplitude and spectral index of primordial power spectrum $A_{s}=2.114\times 10^{-9}$ and $n_{s}=0.9698$, and two DE EoS parameters $\omega_{0}=-0.38$ and $\omega_{a}=-4.8$. Same as DMBI and $f(R)$ gravity models, we use the same method to work out the CSMD of DDE, and find that the variation of the CSMD is largely dominated by the values of six basic parameters $\Omega_{b}h^{2}$, $\Omega_{c}h^{2}$, $\theta_{MC}$, $\tau$, $A_{s}$ and $n_{s}$. Although $\omega_{0}$ and $\omega_{a}$ is loosely constrained by CMB data (constrained $\omega_{0}$-$\omega_{a}$ parameter space is large), different values of $\omega_{0}$ and $\omega_{a}$ hardly affect the CSMD. For instance, in the left panel of Fig.3, $\omega_{0}=-0.38$ and $\omega_{a}=-4.8$ plus the $\Lambda$CDM and DDE best fits gives completely different CSMDs. Choosing the $\Lambda$CDM best fit, $(\omega_{0},\omega_{a})=(-0.38,-4.8)$ and $(\omega_{0},\omega_{a})=(-1,-1)$ gives very similar results in the logarithmic space. In the medium and right panels of Fig.3, we verifies that taking same best fits of $\Lambda$CDM and DDE, respectively, choosing different DE EoS parameter pair just produces very limited differences. After scanning the DDE parameter space, we find clearly that DDE also can not explain this tension, but its best fit can help increase the value of CSMD and become closer to JWST data points (see the left panel of Fig.3). The reason that the result in Ref.Menci:2022wia is different from ours is that they do not implement an appropriate cosmological constraint based on the Planck CMB data.

The result from $f(R)$ gravity prompts us to study the environmental effect of JWST galaxies on the CSMD. The most straightforward method is replacing the Press-Schechter HMF with the EPS formalism in the framework of $\Lambda$CDM, where the sole parameter $\delta_{nl}$ characterizes the nonlinear environmental effect of a high redshift halo. In the bottom right panel, we calculate the maximal CSMDs in the redshift range $z\in[9,11]$ for the EPS model. We find that neither overlarge ($\delta_{nl}=1$) nor too small ($\delta_{nl}=0.1$) explain JWST observations and that the larger $\delta_{nl}$ is, the larger the CSMD is. Since the total sky area covered by the JWST initial observation is large enough ($\sim 40$ armin²) Labbe:2022 , we can not rule out this possibly local environmental effect. However, unfortunately, there is no $\delta_{nl}$ passing two data points simultaneously.

Recently, the early data release of JWST reveals the possible existence of high redshift galaxies. What is interesting is these galaxies in the redshift range $z\in[7,11]$ exhibit the overlarge star formation rate, which is incompatible with the prediction of the standard cosmology. This may indicate that JWST data contain the signal of new physics.

In this study, we try to resolve this tension with alternative cosmological models including DMBI, $f(R)$ gravity and DDE. We find that in light of the precision of current cosmological constraint from Planck-2018 CMB data, these models all fail to explain this large tension. Specifically, for DMBI, the coupling strength $\sigma_{\rm DM-b}$ between DM and baryons hardly affects the CSMD. For $f(R)$ gravity, the effect of varying $f_{R0}$ on the CSMD is too small to relive the tension. For DDE, although the constrained DE EoS parameter space is large, different parameter pair $(\omega_{0},\omega_{a})$ just produces very limited differences in the CSMD. Interestingly, a large interacting DM fraction and a large deviation from Einstein’s gravity can both generate a large CSMD.

A possible scenario to escape from current cosmological constraints is the EPS formalism, where we consider the local environmental effect on the CSMD. We find that an appropriate value of nonlinear environmental overdensity of a high redshift halo can well explain the CSMD discrepancy. However, we do not find an EPS model that can simultaneously explain two data points.

In the near future, JWST will bring more useful data to human beings, so that we can extract more physical information to uncover the mysterious veil of nature.

DW warmly thanks Liang Gao, Jie Wang and Qi Guo for helpful discussions. We thank Hang Yang for letting us notice the JWST related works. This study is supported by the National Nature Science Foundation of China under Grants No.11988101 and No.11851301.