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

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 equivalent to Omega h(2), denoted by R-chi = 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 similar or equal to 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 similar or equal to O(0.01).

Automated summary

A simple analysis was conducted on the sensitivity of big-bang nucleosynthesis to light dark matter generated by the thermal freeze-in mechanism. The study found that the ratio of effective neutrino number shift to dark matter relic density can be used as a visualization tool to test the generation of warm dark matter. This method is particularly useful in scenarios involving cold-plus-warm dark matter compositions.