Reheating after Starobinsky Inflation in the Jordan Frame

TL;DR

This paper studies gravitational reheating in the Starobinsky inflation model within the Jordan frame, showing how Ricci scalar oscillations produce particles and determining the reheating temperature, while comparing Jordan and Einstein frame interpretations.

Contribution

It provides a detailed analysis of gravitational reheating in the Jordan frame of the Starobinsky model, including backreaction effects and frame comparison, which are novel contributions.

Findings

Reheating temperature estimated at ~2 x 10^9 GeV.

Ricci scalar oscillations damp exponentially due to particle backreaction.

Jordan and Einstein frames yield different microphysical predictions for reheating.

Abstract

We investigate gravitational reheating in the Starobinsky model in the Jordan frame, where inflation is driven by an $R^2$ modification of gravity with no explicit inflaton field. In this description, reheating proceeds exclusively through gravitational particle production triggered by the oscillations of the Ricci scalar after the end of inflation. We analyze the post-inflationary background evolution and show that an effective fluid emerging from the modified gravitational dynamics behaves as pressureless matter during the oscillatory phase. Including the backreaction of the produced particles, we demonstrate that the Ricci scalar oscillations acquire an exponential damping, consistently terminating particle production. Solving the coupled background and Boltzmann equations, we obtain a reheating temperature $T_{\mathrm{reh}} \sim 2 \times 10^{9}$ GeV. We finally compare the Jordan and Einstein frame descriptions and argue that, although classically equivalent, they can lead to distinct microphysical interpretations and quantitative predictions for reheating once quantum effects are taken into account.