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

## TL;DR

This paper explores how small-scale variations in dark matter models influence CMB spectral distortions, proposing that future measurements could distinguish between different dark matter candidates by analyzing these distortions.

## Contribution

It introduces a method to use CMB spectral distortions as a probe for small-scale dark matter power spectrum deviations in various alternative dark matter models.

## Key findings

- Alternative dark matter models cause measurable changes in the CMB y-parameter.
- Deviations range from 2% to 7% depending on the model and parameters.
- Upcoming experiments like PIXIE could potentially detect these deviations.

## Abstract

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.