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.

arXiv comment23 pages, 10 figures

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