Simple estimate of BBN sensitivity to light freeze-in dark matter

TL;DR

This paper analyzes how light dark matter produced by thermal freeze-in affects big-bang nucleosynthesis, showing a simple relation between neutrino number shift and DM relic density, and discusses implications for warm and cold-plus-warm DM scenarios.

Contribution

It introduces a simple ratio that links BBN sensitivity to light freeze-in dark matter, independent of particle mass and coupling, aiding in testing DM production mechanisms.

Findings

The ratio R_χ cancels decaying particle mass and coupling effects.

A shift of ΔN_ν ≈ 0.1 cannot come from a single warm DM under Lyman-α constraints.

In cold-plus-warm DM scenarios, R_χ can test freeze-in mechanisms with ΔN_ν ≈ 0.01.

Abstract

We provide a simple analysis of the big-bang nucleosynthesis (BBN) sensitivity to the light dark matter (DM) generated by the thermal freeze-in mechanism. It is shown that the ratio of the effective neutrino number shift $\Delta N_{\nu}$ over the DM relic density $\omega\equiv \Omega h^2$, denoted by $R_\chi\equiv\Delta N_\nu/\omega$, cancels the decaying particle mass and the feeble coupling, rendering therefore a simple visualization of $\Delta N_{\nu}$ at the BBN epoch in terms of the DM mass. This property drives one to conclude that the shift with a sensitivity of $\Delta N_{\nu}\simeq \mathcal{O}(0.1)$ cannot originate from a single warm DM under the Lyman-$\alpha$ forest constraints. For the cold-plus-warm DM scenarios where the Lyman-$\alpha$ constraints are diluted, the ratio $R_\chi$ can be potentially used to test the thermal freeze-in mechanism in generating a small warm component of DM and a possible excess at the level of $\Delta N_{\nu}\simeq \mathcal{O}(0.01)$.