Is leptogenesis during gravitational reheating flavourful?

We examine the impact of charged lepton Yukawa equilibration on leptogenesis during gravitational reheating. During the post-inflationary era, the inflaton field is assumed to oscillate around the minimum of a monomial potential, leading to the gravitational production of Standard Model (SM) particles, constituting the radiation bath. The heavy right-handed neutrinos (RHN), responsible for generating baryon asymmetry via leptogenesis, are also produced through graviton-mediated scattering of the homogeneous inflaton field and thermal bath, as well as from the the inverse decay of the bath particles. By considering both minimal and non-minimal gravitational contributions to SM, we demonstrate that flavour effects can be safely neglected in the minimal reheating scenario. However, with large non-minimal coupling, these effects may become important, depending on the choice of the RHN mass. We identify the corresponding viable parameter space that satisfies the observed baryon asymmetry in each case.