The Cosmology of Atomic Dark Matter

TL;DR

Atomic DM introduces a hidden hydrogen-like sector with four key parameters $m_D$, $\alpha_D$, $B_D$, and $\xi$ that delays kinetic decoupling and creates a Dark-Acoustic-Oscillation scale $r_{DAO}$. The authors develop a detailed atomic-physics treatment using an Effective Multi-Level Atom for dark recombination and solve the coupled Boltzmann equations for DM and dark radiation, including drag and diffusion effects, to predict the DAO imprint on the matter power spectrum and distinctive CMB signatures. They show that small-scale power is suppressed and that dark-photon free-streaming can produce nonuniform phase shifts and amplitude suppression in the CMB, with Ly-$\alpha$ data constraining the viable region to $B_D\gtrsim\mathcal{O}(10)$ keV in much of the parameter space; halo ellipticity and cooling constraints further shape viability. While some regions can address dwarf-galaxy tensions via a larger minimal halo mass and velocity-dependent self-interactions, direct-detection scenarios remain highly constrained and difficult to reconcile with astrophysical bounds. The framework provides a robust cosmological and astrophysical testbed for atomic DM and motivates further work on Ly-$\alpha$ simulations, dark magnetic fields, and partial coupling to the SM.

Abstract

While, to ensure successful cosmology, dark matter (DM) must kinematically decouple from the standard model plasma very early in the history of the Universe, it can remain coupled to a bath of "dark radiation" until a relatively late epoch. One minimal theory that realizes such a scenario is the Atomic Dark Matter model, in which two fermions oppositely charged under a new U(1) dark force are initially coupled to a thermal bath of "dark photons" but eventually recombine into neutral atom-like bound states and begin forming gravitationally-bound structures. As dark atoms have (dark) atom-sized geometric cross sections, this model also provides an example of self-interacting DM with a velocity-dependent cross section. Delayed kinetic decoupling in this scenario predicts novel DM properties on small scales but retains the success of cold DM on larger scales. We calculate the atomic physics necessary to capture the thermal history of this dark sector and show significant improvements over the standard atomic hydrogen calculation are needed. We solve the Boltzmann equations that govern the evolution of cosmological fluctuations in this model and find in detail the impact of the atomic DM scenario on the matter power spectrum and the cosmic microwave background (CMB). This scenario imprints a new length scale, the Dark-Acoustic-Oscillation (DAO) scale, on the matter density field. This DAO scale shapes the small-scale matter power spectrum and determines the minimal DM halo mass at late times which may be many orders of magnitude larger than in a typical WIMP scenario. This model necessarily includes an extra dark radiation component, which may be favoured by current CMB experiments, and we quantify CMB signatures that distinguish an atomic DM scenario from a standard $Λ$CDM model containing extra free-streaming particles. [Abridged]

Figures (24)

• Figure 1: Effective number of dark sector relativistic degrees of freedom at the time of nucleosynthesis as a function of $\alpha_D$ and $B_D$ for dark atoms with mass $m_D=1$ GeV. Here, we have fixed $\xi_{\text{BBN}}=0.5$. We also display the consistency constraint given by Eq. \ref{['consistency_c']} above which dark atoms do not exist.
• Figure 2: Joint BBN constraints on the present-day dark sector temperature and on the effective number of dark sector relativistic degrees of freedom at the time of nucleosynthesis. As indicated, we display contours corresponding to 1-, 2-, and 3-$\sigma$ constraints.
• Figure 3: Comparison between recombination rates. We have chosen the dark sector parameters such that they match those of regular atomic hydrogen. We plot the approximate recombination rate given by Eq. (\ref{['rate_spitzer']}) (green short-dashed line) as well as our rate computed according to Eq. (\ref{['exact_rec_rate']}) including all shells up to $n_{\rm max}=250$ (red long-dashed line). For comparison, we also show the recombination rate given in Ref. 1991AA...251..680P corrected by a fudge factor of 1.14 as used in RecfastSeager:1999bc (black solid line). Top Panel: We compare the rates when the DM and DR are in thermal equilibrium such that $T_{DM}=T_D$. Lower Panel: Similar to the top panel but with $T_{DM}=0.01T_D$.
• Figure 4: Comparison between the rates of different energy-exchange mechanism. We display the rates for Compton heating (solid, black), photo-recombination cooling (short-dashed, blue), and free-free cooling (dotted, green). We also show the Hubble expansion rate (long-dashed, red). The upper panel displays the evolution of the thermal rates for an atomic DM model with $\Upsilon_{BF}\sim700$ and $\Upsilon_R\sim6\times10^{-6}$, the middle panel has $\Upsilon_{BF}\sim280$ and $\Upsilon_R\sim400$, while the lower panel shows the evolution for a model with $\Upsilon_{BF}\sim5\times10^{-4}$ and $\Upsilon_R\sim4$.
• Figure 5: Comparison between our improved treatment of dark recombination and the standard treatment. We display results for a relatively strongly-coupled dark sector with $\Upsilon_{\rm R}\sim6\times10^{-6}$ and $\Upsilon_{\rm BF}\sim700$. The upper panel shows the evolution of the ionization fraction as a function of redshift while the lower panel shows the corresponding evolution of the DM and DR temperatures.