Inflaton Self Resonance, Oscillons, and Gravitational Waves in Small Field Polynomial Inflation

Abstract

In this work, we investigate the post-inflationary dynamics of a simple single-field model with a renormalizable inflaton potential featuring a near-inflection point at a field value $\phi_0$. Due to the concave shape of the scalar potential, the effective mass of the inflaton becomes imaginary during as well as for some period after slow-roll inflation. As a result, in the initial reheating phase, where the inflaton oscillates around its minimum with a large amplitude, some field fluctuations grow exponentially; this effect becomes stronger at smaller $\phi_0$. This aspect can be analyzed using the Floquet theorem. We also analytically estimate the backreaction time after which the perturbations affect the evolution of the average inflaton field. In order to fully analyze this non-perturbative regime, we perform a (classical) lattice simulation, which reveals that the exponential growth of field fluctuations can fragment the system. This leads to a large amount of non-Gaussianity at very small scales, but the equation of state remains close to matter-like. The evolution of the background field throughout the fragmentation phase can be understood using the Hartree approximation. For sufficiently small $\phi_0$ soliton-like objects, called oscillons in the literature, are formed. This leads to areas with high local over-density, $\delta \rho \gg \bar\rho$ where $\bar\rho$ is the average energy density. We speculate that this could lead to the formation of light primordial black holes, with lifetime $\gtrsim 10^{-19} \text{sec}$. Other possibly observational consequences, in particular gravitational waves in the $\text{MHz} - \text{GHz}$ range, are discussed as well. Although a complete analytical study is difficult in our case, we obtain a power law scaling for the potential observables on $\phi_0$.