Gravitational reheating in quintessential inflation

Abstract

We provide a detailed study of gravitational reheating in quintessential inflation generalizing previous analyses only available for the standard case when inflation is followed by an era dominated by the energy density of radiation. Quintessential inflation assumes a common origin for inflation and the dark energy of the Universe. In this scenario reheating can occur through gravitational particle production during the inflation-kination transition. We calculate numerically the amount of the radiation energy density, and determine the temperature $T_*$ at which radiation starts dominating over kination. The value of $T_*$ is controlled by the Hubble parameter $H_0$ during inflation and the transition time $\Delta t$, scaling as $H_0^2 [\ln(1/H_0\Delta t)]^{3/4}$ for $H_0 \Delta t \ll1$ and $H_0^2 (H_0 \Delta t)^{-c}$ for $H_0\Delta t \gg 1$. The model-dependent parameter $c$ is found to be around 0.5 in two different parametrizations for the transition between inflation and kination.