How warm are non-thermal relics? Lyman-$\alpha$ bounds on out-of-equilibrium dark matter

TL;DR

This paper analyzes the linear matter power spectrum of out-of-equilibrium non-thermal dark matter, deriving bounds from Lyman-$eta$ observations, and provides a mapping to translate warm dark matter constraints to various non-thermal scenarios.

Contribution

It introduces a mapping method to relate warm dark matter Lyman-$eta$ bounds to out-of-equilibrium non-thermal dark matter models without complex non-linear computations.

Findings

Bounds on dark matter mass range from EeV to sub-keV depending on production mechanism.

The cutoff scale in the power spectrum is determined by the dark matter's equation of state.

The method applies to various production scenarios including decay and freeze-in processes.

Abstract

We investigate the power spectrum of Non-Cold Dark Matter (NCDM) produced in a state out of thermal equilibrium. We consider dark matter production from the decay of scalar condensates (inflaton, moduli), the decay of thermalized and non-thermalized particles, and from thermal and non-thermal freeze-in. For each case, we compute the NCDM phase space distribution and the linear matter power spectrum, which features a cutoff analogous to that for Warm Dark Matter (WDM). This scale is solely determined by the equation of state of NCDM. We propose a mapping procedure that translates the WDM Lyman-$\alpha$ mass bound to NCDM scenarios. This procedure does not require expensive ad hoc numerical computations of the non-linear matter power spectrum. By applying it, we obtain bounds on several NCDM possibilities, ranging from $m_{\rm DM}\gtrsim {\rm EeV}$ for DM production from inflaton decay with a low reheating temperature, to sub-keV values for non-thermal freeze-in. We discuss the phenomenological implications of these results for specific examples which include strongly-stabilized and non-stabilized supersymmetric moduli, gravitino production from inflaton decay, $Z'$ and spin-2 mediated freeze-in, and non-supersymmetric spin-3/2 DM.