Pushing the Limits of Atomic Dark Matter: First-Principles Recombination Rates and Cosmological Constraints

TL;DR

This work extends atomic dark matter (aDM) phenomenology beyond SM-like benchmarks by computing recombination coefficients and radiative transition rates from first principles for arbitrary dark electron/proton masses $m_{e_D}, m_{p_D}$ and dark fine-structure constant $\alpha_D$ up to $\alpha_D \lesssim 0.3$, and then validating when Standard Model (SM) scalings suffice. It demonstrates that SM-scaled recombination rates, especially the key $\alpha_{21}$ coefficient, reproduce the first-principles results to within a few percent across hydrogen-like to positronium-like regimes, with ground-state bound-bound deviations arising from center-of-mass momentum transfer. The authors incorporate these rates into a cosmological analysis using Planck and ACT DR6 data, DESI BAO, and Pantheon+, and derive the most stringent large-scale constraints on aDM to date: $\Delta N_D \lesssim 0.16$ and $r_{DAO}$ constrained to the $\mathcal{O}$(few to ten) Mpc range depending on the atomic fraction $f_D$. These results significantly narrow the viable aDM parameter space and validate the use of SM-scaled rates for cosmological studies, while highlighting the DAO-scale sensitivity of high-$\ell$ CMB measurements to dark sector physics.

Abstract

Minimal atomic dark matter with its distinctive cooling mechanisms offers an instructive framework for understanding the potential impact of dark matter on small-scale structure formation and early cosmology. The model consists of two fermions with opposite charges under a hidden Abelian gauge symmetry $U(1)_{D}$ and masses $m_{p_{D}}$ and $m_{e_{D}}$, respectively. Analogous to hydrogen in the Standard Model, these fermions interact via their own electromagnetic-like force, with a dark fine structure constant denoted by $α_{D}$, and can bind into neutral atomic (and molecular) dark states. Previous work has largely focused on the benchmark scenario where the dark sector mirrors ordinary matter, with $m_{e_{D}}$ near the electron mass, $m_{p_{D}}$ near the proton mass, and $α_{D}\sim 1/137$. We extend this analysis by investigating dark recombination and cooling physics across the full parameter space of masses and couplings. Combining Cosmic Microwave Background (CMB) measurements from Planck and ACT with BAO and Pantheon+ data, we place new constraints on the atomic dark matter parameter space, identifying regions where acoustic damping and recombination dynamics leave observable imprints on the CMB.

Figures (10)

• Figure 1: Fractional difference between the first-principles calculation of the recombination coefficient $\alpha_{21}$ and the value obtained from scaling the SM result in \ref{['eqn:alpha-scaled']} when setting the dark electron and dark proton masses to their SM values (solid lines) and when setting them both equal to SM electron mass to obtain dark positronium (dashed lines). We show three different temperatures: $T_{\gamma} = E_n$ (black), $T_{\gamma} = 0.1 E_n$ (blue), and $T_{\gamma} = 0.01 E_n$ (red). In all cases, $E_n = B_{H_{D}} / n^2$ with $n=2$ and the matter-radiation ratio is $\mathcal{R}_{m} = 0.1$. We note that for $\mathcal{R}_{m} = 1.0$ these deviations can be as high as 3% for $\alpha_{D}\simeq 0.3$.
• Figure 2: Fractional difference between the first-principles calculation of the bound-bound transition rate to the value obtained from scaling the SM result in \ref{['eqn:SM_scaling']} versus $\alpha_{D}$ at radiation temperature $T_\gamma = B_{H_{D}} = \alpha_{D}^2 \mu_{D}/2$ and a matter-radiation temperature ratio of $\mathcal{R}_{m} = 0.1$, when setting the dark electron and dark proton masses to their SM values (solid lines), and when setting them both equal to SM electron mass to obtain positronium (dashed lines). We consider two examples of photo-absorption processes, specifically $2,1 \rightarrow 3,0$ and $1,0 \rightarrow 2,1$ (left) as well as the stimulated emission processes, specifically $3,0 \rightarrow 2,1$ and $2,1 \rightarrow 1,0$ (right).
• Figure 3: Fractional difference between the bound-bound transition rates and the value obtained from scaling the SM result for positronium masses and large coupling ($\alpha_{D}=0.3$). We show many transitions at three different physical temperatures, with the radiation temperature always fixed at $T_\gamma \propto B_{H_{D}} = \alpha_{D}^2 \mu_{D}/2$. We show absorption transitions up to $n_f =6$ (top) as well as emission processes up to $n=6$ (bottom). Transitions to the ground state for emission show the most significant deviations of $\sim \mathcal{O}(1)$.
• Figure 4: Constraints at 68% and 95% C.L. on the $\Lambda \text{CDM}$ parameters from the P-ACT-LBS dataset combination for both CDM (green) and aDM (blue) with $f_{D}=1$, $m_{p_{D}}=1$ GeV. The preferred ranges of $H_{0}$ and $\Omega_{\mathrm{dm}}h^{2}$ extend to higher values than allowed in CDM, and the preferred values of $n_{s}$ and $\Omega_{b}h^{2}$ are shifted to slightly higher values.
• Figure 5: Constraints at 68% and 95% C.L. on $H_{0}$ and $\Omega_{\mathrm{dm}}h^{2}$ for aDM with $f_{D}=1\ \mathrm{GeV}$ and $m_{p_{D}}=1\ \mathrm{GeV}$ from both P-LBS and P-ACT-LBS dataset combinations. Larger $H_{0}$ and $\Omega_{\mathrm{dm}}h^{2}$ are allowed by Planck than ACT.