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

arXiv comment7 pages, 1 figure; more discussions and references added, final version published in the journal

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• Probing Physics Beyond the Standard Model: Limits from BBN and the CMB Independently and Combined
• Lyman-$\alpha$ constraints on freeze-in and superWIMPs
• Neutrino Magnetic Moments Meet Precision $N_{\mathrm{eff}}$ Measurements
• Dark matter produced from right-handed neutrinos
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• Impact of freeze-in on dark matter isocurvature
• Phenomenology of Dirac neutrino EFTs up to dimension six
• Searching for dark radiation at the LHC