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

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 $\Delta N_{\nu }\simeq \mathcal{O}(0.01)$.

Comments: 7 pages, 1 figure; more discussions and references added, final version published in the journal