The effects of the small-scale behaviour of dark matter power spectrum on CMB spectral distortion

After numerous astronomical and experimental searches, the precise particle nature of dark matter is still unknown. The standard Weakly Interacting Massive Particle(WIMP) dark matter, despite successfully explaining the large-scale features of the universe, has long-standing small-scale issues. The spectral distortion in the Cosmic Microwave Background(CMB) caused by Silk damping in the pre-recombination era allows one to access information on a range of small scales $0.3 \, {\rm Mpc} < k < 10^4 \, \rm Mpc^{-1}$, whose dynamics can be precisely described using linear theory. In this paper, we investigate the possibility of using the Silk damping induced CMB spectral distortion as a probe of the small-scale power. We consider four suggested alternative dark matter candidates---Warm Dark Matter (WDM), Late Forming Dark Matter, Ultra Light Axion dark matter and Charged Decaying Dark Matter; the matter power in all these models deviate significantly from the $\Lambda$CDM model at small scales. We compute the spectral distortion of CMB for these alternative models and compare our results with the $\Lambda$CDM model. We show that the main impact of alternative models is to alter the sub-horizon evolution of the Newtonian potential which affects the late-time behaviour of spectral distortion of CMB. The $y$-parameter diminishes by a few percent as compared to the $\Lambda$CDM model for a range of parameters of these models: LFDM for formation redshift $z_f = 10^5$ (7\%); WDM for mass $m_{\rm wdm} = 1 \, \rm keV$ (2\%); CHDM for decay redshift $z_{\rm decay} = 10^5$ (5\%); ULA for mass $m_a = 10^{-24} \, \rm eV$ (3\%). We also briefly discuss the detectability of this deviation in light of the upcoming CMB experiment PIXIE, which might have the sensitivity to detect this signal from the pre-recombination phase.