Inflaton Self Resonance, Oscillons, and Gravitational Waves in Small Field Polynomial Inflation (2501.13811v1)

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 $\phi_0$.

• The paper investigates post-inflationary dynamics, including inflaton self-resonance and oscillon formation, in a small-field polynomial inflation model using analytical estimates and lattice simulations.
• It finds that field fluctuations grow exponentially due to the potential's properties, fragmenting into localized oscillons that create regions of high energy density.
• These overdensities could potentially lead to the formation of primordial black holes capable of generating gravitational waves in the observable MHz-GHz frequency range.

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

The paper entitled "Inflaton Self Resonance, Oscillons, and Gravitational Waves in Small Field Polynomial Inflation" authored by Manuel Drees and Chenhuan Wang investigates the post-inflationary dynamics of a single-field model with a small-field polynomial inflaton potential. Specifically, the authors explore the phenomenon of inflaton self-resonance, the formation of soliton-like oscillons, and potential gravitational wave production in this cosmological context.

The model posited features a renormalizable potential characterized by a near-inflection point at a particular field value, denoted as $\phi_0$. An intriguing aspect of this potential is its concave nature, which implies an imaginary effective inflaton mass both during and immediately following the period of slow-roll inflation. This leads to significant consequences for the reheating phase, where the inflaton oscillates with large amplitude around its minimum. The field fluctuations exhibit exponential growth, a phenomenon that is more pronounced for smaller values of $\phi_0$. The Floquet theorem is utilized to analyze the dynamics involved during this self-resonance regime.

To quantify the influence of perturbations on the average inflaton field's evolution, the authors derive an analytical estimate for the back-reaction time and employ a classical lattice simulation. The lattice simulation reveals that exponential growth of field fluctuations can lead to fragmentation of the system into highly localized, non-linear structures called oscillons. Despite the nonlinear dynamics, the equation of state of the post-inflationary universe remains close to being matter-like.

A particularly intriguing result of this paper is the formation of oscillons and the associated enhancement in local energy densities, resulting in regions of high over-density. These overdensities prompt speculation about the potential for primordial black hole formation. Given certain conditions, these black holes could persist with lifetimes longer than $10^{-19}$ seconds, thus potentially contributing to cosmological gravitational waves observable today in the $\si{\mega\hertz}-\si{\giga\hertz}$ range.

While a comprehensive analytical treatment of the phenomena is challenging due to the complex non-linear interactions in the model, the authors present a power-law scaling prediction for potential observables related to $\phi_0$. This paper contributes to the understanding of cosmological dynamics following inflation, specifically in the context of small-field models with significant implications for primordial structure formation and gravitational wave backgrounds. Future work might incorporate these findings into broader models of cosmic inflation and explore observational windows for the resulting gravitational waves.