CMB Spectral Distortions from Resonant Conversions in Atomic Dark Sectors

TL;DR

This paper investigates atomic dark sectors with a kinetically mixed massless dark photon and analyzes their imprint on the cosmic microwave background (CMB). By solving Boltzmann equations for energy transfer between the visible and dark sectors, it derives relic abundances and updated $\Delta N_{ m eff}$ constraints in hydrogen and positronium limits, including an intriguing island in the latter where $N_{ m eff}$ is suppressed. The authors then model the dark and visible photon plasmas and identify a resonance when their plasma masses match, which can occur during the dark recombination epoch and induce resonant $\gamma \leftrightarrow \gamma_D$ conversions. Using the Landau-Zener formalism and a pre-recombination μ- and $\rho_{\rm eff}$-based distortion framework, they translate the resonance dynamics into measurable CMB spectral distortions, deriving current COBE/FIRAS limits on the milli-charge $q_D$ (roughly $10^{-7}$–$10^{-6}$) and projecting substantial improvements for future missions like FOSSIL (down to $q_D \sim 10^{-9}$). Their results show complementary constraints: spectral distortions can close gaps left by $N_{ m eff}$ and SN1987A in the positronium limit, while in the hydrogen limit no current spectral-distortion-based unconstrained region remains; overall, resonant conversions in atomic dark sectors provide a powerful probe of hidden electromagnetism with future space-based distortions missions.

Abstract

Dark sectors consisting of atomic constituents (electrons, protons, and photons) offer a well-motivated extension to the Standard Model while providing multiple avenues for phenomenological study. In this work, we explore the impact of conversions between the dark and Standard Model photons in the primordial CMB spectral distortion epoch ($10^3 \lesssim z \lesssim 10^6$). These conversions are resonantly enhanced when the induced thermal masses of both photonic species are equal, thus leading to the possibility that sizeable distortions can be produced. To this end, we solve the Boltzmann equation at early times to determine the (irreducible) freeze-in or freeze-out abundance of dark photons. This procedure also allows us to update the limits on generic milli-charged dark sectors using the ACT DR6 bound on the number of effective radiative degrees of freedom ($N_{\rm eff}$). By then modeling the evolution of the thermal masses in both sectors, we compute the primordial CMB distortion using the Landau-Zener formalism. We find that when the dark electron and proton are roughly similar in mass (the positronium limit), current spectral distortion data from the COBE/FIRAS instrument is able to rule out novel regions of parameter space. We also forecast bounds from the proposed FOSSIL satellite, finding that spectral distortions can also be used to probe the ultra-low dark electric charge regions of parameter space, which are difficult to investigate by other means.

Figures (6)

• Figure 1: $N_{\rm eff}$ contours in the $m_{\rm e_D}-q_{\rm D}$ parameter space for the hydrogen limit (left) and positronium limit (right). In each panel, the hatched areas indicate sections of the parameter space that are constrained from the combined Planck+ACT+LSS+BBN data at 2$\sigma$ACT2025 ($N_{\rm eff} > 3.11$), with the red contour lines highlighting the boundary between the allowed and ruled-out areas. As noted in the main text, there is a region of parameter space in the positronium limit with $2 \,\, {\rm MeV}\lesssim m_\chi \lesssim 9 \,\, {\rm MeV}$ and $q_{\rm D} \gtrsim 2\times10^{-8}$ unconstrained by $\Delta N_{\rm eff}$. This region corresponds to scenarios where the dark sector thermalizes with the photons at early times, but the annihilation of the dark sector fermions happens in between neutrino decoupling and electron-positron annihilation.
• Figure 2: Evolution of the temperature ratios $T_{\nu}/T_{\gamma}$ and $T_{\rm D}/T_{\gamma}$ as a function of $T_{\gamma}$ in the positronium limit for the parameter point $m_{\rm e_{D}} = 5.18~\rm{MeV}$ and $q_{\rm D} = 10^{-5}$, chosen to lie within the so-called 'island' described in the main-text. The annihilation of dark fermions heats the photons, lowering $T_{\nu}/T_{\gamma}$ from its SM value. The dark sector does not fully decouple prior to electron-positron annihilation and so $T_{\rm D}> T^{\rm SM}_{\nu}$ at late times.
• Figure 3: One dimensional slices of the $N_{\rm eff}$ contours shown in Figure \ref{['fig:neff_contour']} for different dark proton to dark electron mass ratios. The gray band corresponds to the 95% CL of the most recent combined CMB and BBN limit from the ACT collaboration ACT2025. As the mass ratio increases, the value of $N_{\rm eff}$ quickly asymptotes to its value in the hydrogen limit.
• Figure 4: Ratio of dark photon plasma mass squared to SM photon plasma mass squared as a function of redshift, for several choices of aDM parameters. The dark proton mass $m_{\rm p_{D}}$ is set equal to $m_{\rm e_{D}}$ in all cases (the positronium limit). The resonant redshift is determined by finding where a given contour crosses the $(m_{\gamma_{\rm D}}/m_{\gamma})^2 = 1$ line.
• Figure 5: Constraints on $q_{\rm D}$ as a function of $m_{\rm e_{D}}$ in the positronium limit ($m_{\rm p_{D}}=m_{\rm e_{D}}$). Left: constraints with $\alpha_{\rm D}=0.01$. Right: constraints with $f_{\rm D}=0.05$. We show current constraints from COBE/FIRAS in solid and projected constraints from FOSSIL in dashed. The constraint from $N_{\mathrm{eff}}$ as measured by ACT is shaded gray, and the constraint from SN1987A is shaded blue.