No quasistable scalaron lump forms afterR2inflation

Abstract

In the Einstein frame picture of Starobinky's ${R}^{2}$ inflation model, cosmic inflation is driven by a slowly rolling inflaton field, called a scalaron, and followed by a coherently oscillating scalaron phase. Since the scalaron oscillates excessively many times in its potential, which has a quadratic minimum and is a little shallower than quadratic on the positive side, it may fragment into long-living localized objects, called oscillons or I balls, due to nonlinear growth of fluctuations before reheating of the Universe. We show that, while parametric self-resonances amplify scalaron fluctuations in the Minkowski background, the growth cannot overcome the decay due to expansion in the Friedmann background after ${R}^{2}$ inflation. By taking into account the backreaction from the metric of spacetime, modes that are larger than a critical scale are indeed amplified and become nondecaying. However, those nondecaying modes are not growing enough to form spatially localized lumps of the scalaron. Thus, reheating processes are unaltered by oscillons/I balls, and they proceed through perturbative decay of the scalaron as studied in the original work.