Gravitational reheating in Starobinsky inflation

We investigate the possibility of achieving post-inflationary reheating exclusively through the gravitational interaction in Starobinsky inflation, which itself assumes nothing but gravity. We consider the possibility that the reheating sector couples to gravity via a non-minimal coupling. Our analysis is performed both in a perturbative and in a non-perturbative approach, where particle production is computed from Bogoliubov coefficients. Our findings indicate that, for a minimal coupling, a reheating temperature $T_\text{reh}\sim 10^{8}$~GeV is obtained, with a reheating duration of approximately 21 $e$-folds. We also show that non perturbative gravitational production during preheating can lead to maximum temperatures of the order of $10^{12}$ GeV. This shows that the gravitational interaction could be the sole responsible for reheating the Universe after inflation, without the need to assume other \emph{ad hoc} inflaton interactions.