Graceful Exit to Radiation Domination in the Starobinsky Model: A Dynamical Realization

Abstract

The Starobinsky model provides a successful realization of inflation and serves as a benchmark for alternative inflationary models. Motivated by its observational success, we investigate the dynamical evolution of the early Universe within this framework. Incorporating radiation production from scalaron decay, we formulate a coupled system of dynamical equations describing scalaron depletion and radiation buildup while ensuring exact energy conservation in the expanding background. In the Friedmann equation, both scalaron and radiation components gravitate, thereby accounting for the backreaction of the generated radiation. Starting with a radiation-free Universe and initial conditions from the standard slow-roll approximations, exact numerical evolution shows that inflationary dynamics is predominantly governed by the scalaron. Despite continuous radiation production, the radiation component remains subdominant, and the slow-roll conditions persist throughout inflation, yielding approximately 60 e-folds. Following inflation, the scalaron enters a damped oscillatory phase accompanied by rapid radiation growth. This transition provides a graceful exit from inflation and a smooth entry into reheating. During reheating, radiation grows continuously as the scalaron energy is depleted, with the radiation energy density ultimately becoming substantially larger than the residual scalaron energy density. This indicates the onset of a hot, radiation-dominated phase, satisfying the Kofman-Yi criterion for successful reheating. Our results demonstrate that the coupled scalaron-radiation dynamics provides a self-consistent realization of graceful exit and the transition to radiation domination in the Starobinsky model.