Reheating processes after Starobinsky inflation in old-minimal supergravity

We study reheating processes and its cosmological consequences in the Starobinsky model embedded in the old-minimal supergravity. First, we consider minimal coupling between the gravity and matter sectors in the higher curvature theory, and transform it to the equivalent standard supergravity coupled to additional matter superfields. We then discuss characteristic decay modes of the inflaton and the reheating temperature $T_{\mathrm{R}}$. Considering a simple model of supersymmetry breaking sector, we estimate gravitino abundance from inflaton decay, and obtain limits on the masses of gravitino and supersymmetry breaking field. We find $T_{\mathrm{R}}\simeq 1.0\times {10}^9$ GeV and the allowed range of gravitino mass as ${10}^4$ GeV $\lesssim m_{3\mathrm{/}2}\lesssim {10}^5$ GeV, assuming anomaly-induced decay into the gauge sector as the dominant decay channel.