Thermal relics as hot, warm and cold dark matter in power-law $f(R)$ gravity

TL;DR

This paper explores how modifications in $f(R)$ gravity affect the properties and bounds of thermal relic dark matter candidates, revealing relaxations in mass constraints and deviations from standard cosmology.

Contribution

It provides an analysis of thermal relics in power-law $f(R)$ gravity, showing how the parameter $eta$ influences relic properties and relaxes standard mass bounds.

Findings

Relativistic and nonrelativistic regimes analyzed for relics.

Mass bounds for neutrinos and WIMPs are relaxed in $f(R)$ gravity.

Framework reduces to General Relativity when $eta o 1^+$.

Abstract

We investigate the thermal relics as hot, warm and cold dark matter in $\mathscr{L}=\varepsilon^{2-2\beta}R^\beta+{16\pi}m_{\text{Pl}}^{-2}\mathscr{L}_m$ gravity, where $\varepsilon$ is a constant balancing the dimension of the field equation, and $1<\beta<(4+\sqrt{6})/5$ for the positivity of energy density and temperature. If light neutrinos serve as hot/warm relics, the entropic number of statistical degrees of freedom $g_{*s}$ at freeze-out and thus the predicted fractional energy density $\Omega_\psi h^2$ are $\beta-$dependent, which relaxes the standard mass bound $\Sigma m_\nu$. For cold relics, by exactly solve the simplified Boltzmann equation in both relativistic and nonrelativistic regimes, we show that the Lee-Weinberg bound for the mass of heavy neutrinos can be considerably relaxed, and the 'WIMP miracle" for weakly interacting massive particles (WIMPs) gradually invalidates as $\beta$ deviates from $\beta=1^+$. The whole framework reduces to become that of GR in the limit $\beta\to 1^+$.