Probing dark matter interactions with 21cm observations

The universe on large scales seems to be well described by the simple cosmological $\Lambda$CDM model. The model reproduces to a high accuracy the statistical properties of both the cosmic microwave background (CMB) anisotropies and the large-scale matter distribution—including the baryon acoustic oscillations (BAO)—using only six parameters [1, 2, 3]. However, this simplicity comes at a price: in order to achieve concordance with observations, the model must invoke two mysterious components, namely, dark matter and dark energy. The standard assumptions for these are, respectively, a collisionless massive particle—the so-called Cold Dark Matter (CDM)—and a cosmological constant ($\Lambda$). Many particle physics models have been designed to include a viable particle candidate for the dark matter; similarly, there is no shortage of gravity theories capable of mimicking the phenomenology of a cosmological constant. However, there is no consensus yet on the nature of either component [4, 5, 6].

Focusing on the dark matter question, we note that generic CDM particle candidates predict structures on all length scales. However, we cannot preclude the possibility that structures may not be present on small length scales not yet accessible to observations. Indeed, several classes of dark matter scenarios predict exactly that. The warm dark matter (WDM) scenarios, for example, are typically characterised by a relatively low particle mass (in the low keV range). Such light masses enable the free-streaming of these particles to erase the primordial seeds for cosmological structure formation, thus leading to a heavily suppressed number of small-scale structures relative to the CDM case [7, 8, 9, 10, 11, 12, 13, 14, 15, 16].

Another interesting possibility are the interacting dark matter (IDM) scenarios, wherein the interaction of the dark matter—with other constituents of the universe or with itself—persists until the primordial nucleosynthesis epoch or later. This class of dark matter also predicts a loss of small-scale structures on cosmologically testable scales, but through collisional damping rather than free-streaming. In addition, IDM scenarios predict the appearance of dark acoustic oscillations, as has been demonstrated in the linear regime of evolution, a strong distinguishing feature of this class of dark matter scenarios from the classic WDM. A variety of IDM scenarios has been investigated in the literature. These include interactions of dark matter with itself [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28], with baryons [27, 29, 28, 30, 31, 32, 33, 34, 35, 36, 37], with photons [27, 38, 28, 39, 40, 32, 31, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50], as well as with neutrinos [27, 28, 51, 52, 53, 45, 54, 55, 56, 57] and more recently with a dark sector radiation species [58, 59, 60, 61, 62, 63, 64, 65, 66].

While both WDM and IDM are often invoked as a possible solution to the observational challenges confronting $\Lambda$CDM on small scales [67], we emphasise that, ultimately, the way to acquire a complete picture of the fundamental nature of dark matter is to reconstruct the matter power spectrum down to the smallest scales and at the highest redshifts possible. Indeed, although both WDM and IDM predict a damped power spectrum in the linear regime and IDM scenarios have additional tell-tale features, the evolution of structure formation in the non-linear regime tends to erase these differences, bringing the observable effects of these scenarios closer to the CDM predictions with time [68]. Hence, the closer the observations are to probing the linear regime of evolution, the better they would be for distinguishing between these scenarios and possibly confirming the particle nature of dark matter.

As technology advances and ever better experiments are built, we gain access to more powerful probes to constrain deviations from $\Lambda$CDM (or perhaps even rule out $\Lambda$CDM itself). In this work, we confirm that measurements of the matter power spectrum $P(k)$ at high redshifts will be a key observable to probe the existence of dark matter interactions and show that 21cm intensity mapping, which traces neutral hydrogen—commonly denoted HI—through its emission from a hyperfine transition to its ground state, will provide a critical tool to do so. Although the all-sky average signal, including redshift information, has already been measured by EDGES [69], which can also be used to constrain dark matter interactions [50], its lack of angular resolution does not allow for intensity mapping. Future observatories such as SKA, however, will have a much better resolution than EDGES and its measurements of the 21cm emission intensity as a function of the angular position will yield density maps similar to maps of the CMB anisotropies [70, 71, 72, 73, 74, 75]. Together with redshift information out to $z\sim 25$, these angular maps will enable the 3D reconstruction of the distribution of emitters in the sky [76]. Thus, high resolution radio surveys to be performed with such instruments as SKA will be ideal to help distinguish between different types of dark matter scenarios.

To make our predictions, we perform a suite of numerical simulations using the public code gadget-4 [77], for several WDM and IDM scenarios as well as CDM which we use as reference. In the case of IDM, we use as a generic example a dark matter-neutrino scattering scenario, as this can help probe very weak dark matter interactions with the Standard Model and might also be related to the neutrino mass generation mechanism [78]. The linear evolution of this IDM scenario is computed using a modified version of class [79, 80] described in Ref. [56], which includes the full Boltzmann hierarchy for massive neutrinos interacting with a heavy dark matter species. Our simulations show that, while the small-scale suppression of the IDM matter power spectrum remains—thereby making the scenario distinguishable from CDM—the dark acoustic oscillations that characterise IDM are washed out by non-linear growth at late times, particularly at redshifts $z\lesssim 10$. The predictions of IDM at late times should therefore resemble those of WDM. Thus, like for the WDM scenarios studied in Ref. [81, 82, 83], one expects future 21cm data to set a limit on the IDM damping scale. Here, we show that using these data would improve the constraints on the elastic dark matter-neutrino scattering cross section by two orders of magnitude with respect to the Lyman-$\alpha$ constraints [57] and four orders of magnitude with respect to CMB+BAO bounds [56].

To quantify just how well future matter power spectrum measurements will be able to distinguish between IDM and WDM scenarios, we investigate also the predictions of these scenarios at higher redshifts. For IDM interaction strengths tuned to mimic as closely as possible the linear predictions of specific WDM masses, we find that the non-linear matter power spectra of these two classes of dark matter scenarios match to a few percent or better at $z\lesssim 10$. Therefore, to distinguish them, one would need percent-level precise measurements at redshifts $z\gtrsim 15$, i.e., just before the dark acoustic oscillations in the matter power spectrum become completely washed out.

The structure of this work is as follows. In Section 2 we present the interacting and warm dark matter scenarios we wish to investigate, while in Section 3 we provide a short overview of the 21cm emission and how the signal is predicted. Section 4 presents a comparison of our interacting and warm dark matter initial conditions and a description of our $N$-body simulations. We present the results of our $N$-body simulations in Section 5. Section 6 contains our conclusions.

We present in this section the interacting dark matter and warm dark matter scenarios investigated in this work. We describe in particular their linear evolution, which is in turn used to set the initial conditions for our numerical simulations in Section 4.

The 21cm line is an electromagnetic spectral line emitted from a spin-flip transition in neutral hydrogen (HI) between the two levels of a hyperfine splitting in the $1s$ state. The transition is usually deemed forbidden under laboratory conditions, but is nonetheless possible to observe in astronomical settings if there is a sufficient abundance of neutral hydrogen.

In the context of standard cosmology after recombination, some 75% of the universe’s baryon content comes in the form of HI. After they have been released by the CMB from the baryon drag at $z\approx 1020$ and cooled sufficiently, the higher-energy triplet state can be excited from the singlet ground state by background photons, collisions between hydrogen atoms, or via an intermediate state after excitation from Lyman-$\alpha$ photons [71]. The ratio of atoms in the two energy levels is usually parameterised in terms of a “spin temperature” $T_{s}$,

where $T_{*}=0.068\,{\rm K}=5.9\cdot 10^{-6}$ eV corresponds to the transition energy between the two states, and the factor of 3 accounts for the degeneracy of the triplet state.

Because of the multitude of processes, such as those listed above, that can alter the spin distribution, the evolution of the ratio $n_{1}/n_{0}$ and hence the spin temperature $T_{S}$ is generally highly non-trivial. Crucially, however, if the spin temperature is higher than the CMB background temperature, i.e., $T_{S}\gtrsim T_{\rm CMB}$, then the 21cm line is observable against the CMB background as a net emission, while the opposite case of $T_{s}\lesssim T_{\rm CMB}$ results in net absorption. This variation of $T_{S}$ relative to $T_{\rm CMB}$ leads to variations in the intensity of the global 21cm signal against the CMB back light as a function of redshift, normally expressed in terms of the differential brightness temperature [71],

where $\tau_{\nu_{0}}$ is the optical depth at the 21cm frequency $\nu_{0}$. Measurements of the gloabl $\delta T_{b}(z)$ can therefore serve as a powerful probe of processes that affect the evolution of the HI content of the universe, from standard effects such as the onset of star formation, to non-standard interactions between hydrogen and the dark sector. See, for example, Ref. [87] for investigations of the latter in relation to the EDGES result.

Furthermore, because the spatial distribution of the underlying dark matter density field is inhomogeneous, the HI density and hence the 21cm signal intensity must also trace this inhomogeneity to a large extent. The 21cm signal can therefore be used to map structures through line intensity mapping. In this endeavour, the intensity of the 21cm line is measured for locations across the sky, similarly to the construction of a CMB map. The mapping does not require individual sources to be resolved, but provides a tracer for the density of atomic hydrogen, which is itself a (biased) tracer of structures. Because the emission is a well-defined line, the redshift can be measured precisely, thereby allowing the distance to be inferred. Together with the angular information, this distance measurement will allow us to reconstruct in 3D the spatial distribution of the HI in the early universe, from which to infer the underlying dark matter density field.

Provided that the particle velocity is not too large, the late-time (i.e., $z\lesssim 100$) evolution of a WDM cosmology should be very similar to that of a previously interacting but now decoupled IDM cosmology tuned to give matching linear predictions in the manner described in Section 2. As a direct consequence of the suppressed linear power on small scales—whether due to free-streaming or collisional damping—the onset of gravitational collapse into structures would be similarly delayed relative to the standard CDM case. Thus, for an IDM scenario with no late-time interaction with baryons and photons, WDM forecasts should be directly translatable to the case of IDM—as we have proposed to do at the end of Section 3.1—without the need to recompute the hydrodynamic evolution of the baryons and/or the HI distribution. This is convenient, as forecasts for how well SKA can distinguish between CDM and WDM cosmolgies via the 21cm brightness temperature power spectrum at $z\approx 3$–5 already exist [81], as discussed above in Section 3.1.

What remains to be done is therefore two-fold. First, we need to confirm that non-linear evolution does tend to bring closer together the gross predictions of a WDM scenario to that of an IDM scenario tuned to match as closely as possible the former’s linear predictions. Second, what observable differences between the two cosmologies remain, and hence whether the 21cm observations can help distinguish WDM from IDM. To this end, we perform a suite of collisionless $N$-body simulations for several WDM and IDM cosmologies, paying particular attention to the high-redshift ($z\gtrsim 10$) predictions, where the differences between them are most likely to remain. We describe briefly the simulation settings below. The simulation results are presented in Section 5.

Figures 4, 5, and 6 summarise our simulation results in a set of matter power spectra at various redshifts.

The first key takeaway is that non-linear evolution causes the difference between CDM, WDM, and IDM cosmologies to diminish with time. This is well illustrated in Fig. 4, where it is evident that despite significant differences at early times ($z\gtrsim 15$), the late-time ($z\lesssim 5$) matter power spectra of these different cosmologies differ only by a few percent. Endowing WDM particles with a thermal velocity kick does not significantly alter the outcome, apart from adding Poisson noise at large wave numbers $k$, as was also noted in Ref. [99]. It is therefore clear that high-precision measurements at high redshifts are a key part of constraining departures from CDM.

Focusing on the $z=3$–5 matter power spectra shown in Fig. 5, we see that a maximum 10%–60% suppression remains for the WDM and IDM cosmologies relative to the reference CDM case in the reference wave number range $0.3\lesssim k/[h/{\rm Mpc}]\lesssim 60$. However, non-linear evolution has completely washed out the characteristic oscillatory features of IDM cosmologies, leading to power spectrum predictions that differ from those of WDM scenarios only by a few percent. Importantly though, the difference between WDM and IDM at these redshifts appears to be smaller than the free-streaming or collision damping suppression of the small-scale power spectrum itself relative to CDM. This means we should also expect the 21cm brightness temperature power spectrum of IDM cosmologies to be characterised by an enhancement in the amplitude relative to the CDM case, where the enhancement increases with interaction strength $u_{\nu\chi}$ in a manner directly relatable to WDM masses via Table 1.¹¹1Note that our CDM and WDM power spectra are not an exact match to those found in Ref. [81]. Specifically, we see a slightly greater small-scale suppression of power in the WDM cosmologies relative to the reference $\Lambda$CDM model. For example the right panel of Fig. 5 shows a 60% suppression in the 1 keV WDM scenario at $k=100\,h$/Mpc and $z=5$; the equivalent result of Ref. [81], displayed in their Fig. 1, finds a 40% suppression. The slightly different $n_{s}$ values adopted in the simulations may have contributed to the discrepancy. However, the most likely explanation is that, unlike Ref. [81], we have not accorded baryons a hydrodynamical treatment, but merely lumped them together with the dark matter as one single collisionless species. This is undoubtedly a drastic simplification. However, for the purpose of demonstrating that the collisionless dark matter in both WDM and IDM cosmologies evolve similarly, it is a sufficient treatment. Furthermore, because neither the WDM nor the IDM has direct, non-gravitational interactions with baryons, full hydrodynamical simulations of these cosmologies should not change the qualitative conclusion that WDM and IDM are phenomenologically very similar at $z\approx 3$–5. Thus we arrive at our second key takeaway: constraints on WDM masses from non-linear structure measurements at $z\approx 3$–5 can be immediately translated to constraints on the equivalent $u_{\nu\chi}$. As demonstrated in Ref. [81], observations by SKA1-LOW will be able to constrain WDM masses to $m_{\rm WDM}\gtrsim 4$ keV, which translates into a limit of $u_{\nu\chi}\lesssim 3.6\cdot 10^{-8}$ for IDM. The strongest constraint on $u_{\nu\chi}$ at the time of writing is $u_{\nu\chi}\lesssim 8\cdot 10^{-6}$ [57] obtained from the Lyman-$\alpha$ forest. Thus, 21cm intensity mapping could improve upon current cosmological constraints on IDM scenarios by at least two orders of magnitude.

Our findings also imply that, in order to distinguish between IDM and WDM, higher-redshift observations are necessary. Indeed, as shown in Fig. 6 (and verified at a higher simulation resolution in Fig. 7 for the 1 keV and $u_{\chi}=8.5\cdot 10^{-7}$ cases), the characteristic dark acoustic oscillations of IDM become discernible at $z\gtrsim 15$, and are, for a fixed redshift, more evident for larger interaction strengths $u_{\nu\chi}$, i.e., smaller equivalent WDM masses. The latter effect is due largely to the dark acoustic acoustic oscillations appearing on smaller length scales as we decrease $u_{\nu\chi}$, where non-linear dynamics kicks in at an earlier time. If we were to decrease $u_{\nu\chi}$ even further to values outside of the range investigated in this work, we would expect the dark acoustic oscillations to be pushed into a $k$ region below the resolution of these simulations; to numerically probe these cases would necessitate dedicated high-resolution simulations.

However, even with the simulations performed for this work, we are able to give conservative estimates of the precision needed in $P(k)$ measurements to distinguish between WDM and IDM scenarios. For the strongest interactions investigated, $u_{\nu\chi}\approx 8.5\cdot 10^{-7}$, only $\sim 10\%$ and $\sim 20$% precision is needed at $z\sim 15$ and $z\sim 30$, respectively, to distinguish it from a WDM cosmology with $m_{\rm WDM}\approx 1$ keV. For the weaker $u_{\nu\chi}\approx 1.75\cdot 10^{-7}$ and its $m_{\rm WDM}\approx 2$ keV equivalent, the precision requirements for distinction tighten to $\sim 5\%$ and $\sim 10$%. Even greater precision would be required for weaker interactions/larger $m_{\rm WDM}$, or we would need to observe at even higher redshifts and/or larger wave numbers.

Using a suite of collisionless $N$-body simulations, we have shown in this work that the observable consequences of interacting dark matter cosmologies closely mimic those of warm dark matter scenarios at redshifts $z\lesssim 10$. This means that cosmological observations at these redshifts sensitive to WDM properties must also be able to probe IDM in a similar manner, and forecasts for future WDM constraints should be easily adaptable to constraints on IDM.

Specifically, we have considered the constraining power of future 21cm line intensity mapping in the context of a dark matter-neutrino interaction scenario. Previous works in the literature showed that the 21cm brightness temperature power spectrum as will be measured by SKA1-LOW will be able to constrain the WDM mass to $m_{\rm WDM}\lesssim 4$ keV [81] with ${\cal O}(1000)$ hours of observation. The analysis of Ref. [82] forecasted constraints that are even stronger by up to a factor of 3.5. Through mapping IDM to WDM simulation outcomes, we find that the more conservative $m_{\rm WDM}\lesssim 4$ eV can be translated to an upper limit on the dark matter-neutrino interaction strength of $u_{\nu\chi}\lesssim 3.6\cdot 10^{-8}$. This represents a forecasted improvement of more than two orders of magnitude with respect to the current constraint from the Lyman-$\alpha$ forest [57], and will likewise tighten by four orders of magnitude current bounds from CMB+BAO [56].

While the observable similarity between WDM and IDM at $z\lesssim 10$ makes it a plus in terms of computational convenience, at the same time it also detracts from our ability to distinguish between these two classes of models observationally. Indeed, we find that in order to obtain a “smoking gun” signal for an IDM scenario, it is necessary to observe the matter power spectrum at redshifts $z\gtrsim 15$ to a precision of $\sim$2–10%, depending on the interaction strength, before the characteristic dark acoustic oscillations of this type of scenarios become completely washed out by non-linear evolution. The weaker the interaction, the more stringent the redshift and precision requirements, as the characteristic dark acoustic oscillations get pushed out to smaller and more non-linear scales with decreasing interaction strength.

The SKA should be able to probe the 21cm signal out to $z\gtrsim 25$ [104, 76] and therefore has the potential to make the distinction between WDM and IDM. Observing at such high redshifts also offers another advantage over lower redshifts: it allows us to reduce the uncertainties introduced by astrophysics in the form of feedback from star formation, supernovae, and galaxy formation, which are important effects at $z\lesssim 10$. At earlier times, the hydrogen found in filaments also has a higher relative importance [88] compared to halos, changing the dependence of the 21cm power spectrum on the halo number, and the HI-to-DM bias at these redshifts would need to be well-modelled. Such predictions would require a dedicated study beyond the scope of this paper, and is therefore left for future work.

We thank Joe Chen for useful discussions on the implementation of thermal velocities. Y³W is supported in part by the Australian Government through the Australian Research Council’s Future Fellowship (project FT180100031). This research includes computations using the computational cluster Katana supported by Research Technology Services at UNSW Sydney. Part of this work was performed on the OzSTAR national facility at Swinburne University of Technology. The OzSTAR program receives funding in part from the Astronomy National Collaborative Research Infrastructure Strategy (NCRIS) allocation provided by the Australian Government.