Simple estimate of BBN sensitivity to light freeze-in dark matter
Shao-Ping Li, Xin-Qiang Li, Xin-Shuai Yan, Ya-Dong Yang
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 $\mathrm{\ensuremath{\Delta}}{N}_{\ensuremath{\nu}}$ over the DM relic density $\ensuremath{\omega}\ensuremath{\equiv}\mathrm{\ensuremath{\Omega}}{h}^{2}$, denoted by ${R}_{\ensuremath{\chi}}\ensuremath{\equiv}\mathrm{\ensuremath{\Delta}}{N}_{\ensuremath{\nu}}/\ensuremath{\omega}$, cancels the decaying particle mass and the feeble coupling, rendering therefore a simple visualization of $\mathrm{\ensuremath{\Delta}}{N}_{\ensuremath{\nu}}$ at the BBN epoch in terms of the DM mass. This property drives one to conclude that the shift with a sensitivity of $\mathrm{\ensuremath{\Delta}}{N}_{\ensuremath{\nu}}\ensuremath{\simeq}\mathcal{O}(0.1)$ cannot originate from a single warm DM under the Lyman-$\ensuremath{\alpha}$ forest constraints. For the cold-plus-warm DM scenarios, where the Lyman-$\ensuremath{\alpha}$ constraints are diluted, the ratio ${R}_{\ensuremath{\chi}}$ 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 $\mathrm{\ensuremath{\Delta}}{N}_{\ensuremath{\nu}}\ensuremath{\simeq}\mathcal{O}(0.01)$.