CMB and 21-cm Signals for Dark Matter with a Long-Lived Excited State

TL;DR

This work introduces dark matter models with collisional long-lived excited states (XDM) and computes the relic excitation fraction $Y_f$ arising from early-universe kinetics. It analyzes how late-time de-excitations deposit energy into the intergalactic medium, altering ionization and thermal histories, and derives observable signatures in the CMB and high-redshift 21-cm signals. The study shows that, for natural cross-sections and mediator parameters, $Y_f$ can be significant, yielding potentially detectable deviations in cosmological observables, while in the specific INTEGRAL-favored region $Y_f$ is smaller; nonetheless, the framework broadens the phenomenology of WIMP-like DM. The results highlight the complementary role of CMB and 21-cm observations in probing nonstandard DM scenarios with excited states, offering a path for future experimental tests.

Abstract

Motivated by the eXciting Dark Matter (XDM) model of Finkbeiner & Weiner, hypothesized to explain the 511 keV signal in the center of the Milky Way, we consider the CMB and 21-cm signatures of models of dark matter with collisional long-lived excited states. We compute the relic excitation fraction from the early universe for a variety of assumptions about the collisional de-excitation cross-section and thermal decoupling. The relic excitation fraction can be as high as 1% for natural regions of parameter space, but could be orders of magnitude smaller. Since the lifetime of the excited state is naturally greater than 10^13s, we discuss the signatures of such relic excitation on cosmic microwave background (CMB) and high-z 21-cm observations. Such models have potentially richer astrophysical signals than the traditional WIMP annihilations and decays, and may have observable consequences for future generations of experiments.

Figures (11)

• Figure 1: Dominant diagram contributing to kinetic equilibrium of $\chi$.
• Figure 2: Dominant diagram contributing to thermal equilibrium of $\phi$.
• Figure 3: The evolution of the excitation fraction with time, for $M_\chi = 1\,{\rm TeV}$, $T_{\rm dec}=100\,{\rm MeV}$, $\delta=1\,{\rm MeV}$ and $\tilde{\sigma}_{mr}=1$ (see Eq. \ref{['eq:app_kd_fid']}). Solutions are shown for the full coupled Boltzmann equations (solid black). We show the results under certain additional approximations as well, in particular with temperature coupling turned off (dashed blue), for the approximation $k_{E} = k_{D} \exp(-\delta/T)$, ignoring the corrections in Appendix \ref{['sec:rates']} (red dotted), and for temperature coupling turned off and$k_{E} = k_{D} \exp(-\delta/T)$ (long-dashed green).
• Figure 4: The residual excitation fraction $Y_f$ as a function of the scattering cross section $\tilde{\sigma}_{mr}$, and decoupling temperature $T_{\rm dec}$, for $M_\chi = 500{\rm ~GeV}$ (solid black) and $M_\chi = 1{\rm ~TeV}$ (dashed red). From top to bottom for each mass, the decoupling temperatures are $T_{\rm dec}$ = 100 MeV, 500 MeV, 1 GeV, and 10 GeV. The 511 keV signal favors $\tilde{\sigma}_{mr} = 0.1$ - $50$ for a 500 GeV WIMP.
• Figure 5: The ionization fraction $x_{i}\equiv n(e^-)/n(H)$ (top), and matter temperature (bottom), for various values of the lifetime, $\tau_{\chi^*}$, with $Y_f$ held fixed. The baseline scenario, with no energy injection from WIMPs, is shown in both panels (thick solid line), and $T_{cmb}$ is included in the bottom panel (dotted line). In all cases we take $Y_f = 10^{-3} \epsilon_{b}$. Note that we ignore the effects of star formation etc. on the ionization fraction and temperature.