Using CMB spectral distrotions to distinguish between dark matter solutions to the small-scale crisis

The dissipation of small-scale perturbations in the early universe produces a distortion in the blackbody spectrum of cosmic microwave background photons. In this work, we propose to use these distortions as a probe of the microphysics of dark matter on scales 1Mpc(-1) less than or similar to k less than or similar to 10(4) Mpc(-1). We consider in particular models in which the dark matter is kinetically coupled to either neutrinos or photons until shortly before recombination, and compute the photon heating rate and the resultant mu-distortion in both cases. We show that the mu-parameter is generally enhanced relative to Lambda CDM for interactions with neutrinos, and may be either enhanced or suppressed in the case of interactions with photons. The deviations from the Lambda CDM signal are potentially within the sensitivity reach of a PRISM-like experiment if sigma(DM-gamma) & 1.1 x 10(-30) (m(DM) GeV) cm(2) and sigma(DM--nu) greater than or similar to 4.8 x 10(-32) (m(DM/)GeV) cm(2) for time-independent cross sections, and sigma(DM-gamma) greater than or similar to 1.8 x 10(-40) (m(DM)/GeV) cm(2) and sigma(0)(DM-nu) greater than or similar to 2.5 x 10(-7) (m(DM) GeV) cm(2) for cross sections scaling as temperature squared, coinciding with the parameter regions in which late kinetic decoupling may serve as a solution to the smallscale crisis. Furthermore, these mu-distortion signals di ff er from those of warm dark matter (no deviation from Lambda CDM) and a suppressed primordial power spectrum (a strongly suppressed or negative mu-parameter), demonstrating that CMB spectral distortion can potentially be used to distinguish between solutions to the small-scale crisis.