Spectral distortions in the decaying QCD dark matter scenario

Abstract

We study the QCD--DM scenario by analyzing the imprint of energy injection from decaying dark-sector particles on the spectral distortions (SDs) of the Cosmic Microwave Background (CMB). We adopt a unified framework capable of describing both relativistic and non-relativistic particles, as well as fast and slow decay regimes. Within this approach, we model exponential, power-law, oscillatory, and two-step decays, computing the resulting $\mu$- and $y$-type distortions across the parameter space spanned by the confinement scale $a_c$, decay rate ${\Gamma }_{\chi }$, energy-transfer efficiency ${\Sigma }_{\chi }$, and velocity $v_{\chi c}$. We find that power-law, oscillatory, and cascade decays can be effectively mapped onto exponential models with appropriate rescaling. The dominant factors controlling SDs are the decay epoch and lifetime, with $v_{\chi c}$ becoming relevant only in the ultra-relativistic limit. FIRAS observations impose tight constraints on early energy injection, with $\mu$-type distortions placing the strongest bounds on ${\Sigma }_{\chi }$. Simultaneous matching of both ${\mu }_{\mathrm{firas}}$ and $y_{\mathrm{firas}}$ breaks the degeneracy between ${\Gamma }_{\chi }$ and ${\Sigma }_{\chi }$, localizing preferred decay rates around ${\Gamma }_{\chi }\lesssim (3.3-4.4)\times 10^{-3}{\mathrm{yr}}^{-1}$ and ${\Sigma }_{\chi }\lesssim 8.5\times 10^{-4}$ for relativistic particles, while fast decays with ${\Gamma }_{\chi }\gtrsim 6.5{\mathrm{yr}}^{-1}$ become observationally negligible. Our results show that CMB spectral distortions are a powerful probe of dark-sector dynamics. Future missions such as PIXIE or PRISM could extend current limits by several orders of magnitude and test previously inaccessible regions of parameter space.

23 pages, 10 figures

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