Freeze-in and freeze-out production of Higgs portal Majorana fermionic dark matter during and after reheating

In this paper, we investigate the production of Majorana fermionic dark matter (DM) via the Higgs portal, considering both freeze-in and freeze-out mechanisms during and after the post-inflationary reheating phase. We assume that the Universe is reheated through the decay of the inflaton ($\phi$) into a pair of fermions $f$ and $\bar f$ via the interaction $y\,\phi\,\bar f\,f$, where $y$ is the dimensionless Yukawa coupling. Our analysis focuses on how the non-standard evolution of the Hubble expansion rate and the thermal bath temperature during reheating influence DM production. Additionally, we examine the impact of electroweak symmetry breaking (EWSB), distinguishing between scenarios where DM freeze-in or freeze-out occurs before or after EWSB. We further explore the viable DM parameter space and its compatibility with current and future detection experiments, including XENONnT, LUX-ZEPLIN (LZ), XLZD, and collider searches. Moreover, we incorporate constraints from the Lyman-$\alpha$ bound to ensure consistency with small-scale structure formation.