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Post-inflationary Dark Matter production and Leptogenesis: Metric versus Palatini formalism

Anish GhoshalZygmunt LalakSupratik PalShiladitya Porey
Jan 2024
We investigate production of non-thermal dark matter particle and heavy sterile neutrino from inflaton during the reheating era which is preceded by a slow-roll inflationary epoch with a quartic potential and non-minimal coupling ($\xi$) between the inflaton and the gravity. We compare our analysis between metric and Palatini formalism. For the latter with $\xi=0.5$ and number of $e$-folds $\sim 60$, $r$ can be as small as $\sim {\cal O}\left(10^{-3}\right)$ which may be validated at $1-\sigma$ CL of prospective future reaches of upcoming CMB observation such as CMB-S4~etc. We identify that permissible range of Yukawa coupling $y_\chi$ between inflaton and fermionic DM $\chi$, to be ${\cal O}\left(10^{-3.5}\right)\gtrsim y_\chi \gtrsim {\cal O}\left(10^{-20}\right)$ for metric formalism and ${\cal O}\left(10^{-4}\right)\gtrsim y_\chi \gtrsim {\cal O}\left(10^{-11}\right)$ for Palatini formalism which is consistent with current PLANCK data and also be within the reach of future CMB experiments. For the scenario of leptogenesis via the decay of sterile neutrino produced from inflaton decay, we also investigate the parameter space of heavy neutrino mass $m_{N_1}$ and Yukawa coupling $y_{N_1}$ of sterile neutrino with inflaton, which are consistent with current CMB data and successful generation of the observed baryon asymmetry of the universe via leptogenesis. In contrast to metric formalism, in the case of Palatini formalism for successful leptogenesis to occur we find that $y_{N_1}$ has a very narrow allowable range and is severely constrained from the consistency with CMB predictions.
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