Gravitational Production of Heavy Particles during and after Inflation

TL;DR

This paper analyzes the gravitational creation of heavy scalar particles during and after inflation across various models, providing analytical formulas and numerical validation, with implications for dark matter.

Contribution

It introduces a simple analytical method to accurately compute gravitational particle production during different inflationary phases, validated by numerical solutions.

Findings

Analytical expressions match numerical results for particle production rates.

Two distinct production phases identified: during and after inflation.

Post-inflation production depends on the inflaton mass relative to Hubble scale.

Abstract

We investigate the gravitational production of a scalar field $\chi$ with a mass exceeding the Hubble scale during inflation $m_\chi \gtrsim H_I$, employing both analytical and numerical approaches. We demonstrate that the steepest descent method effectively captures the epochs and yields of gravitational production in a compact and simple analytical framework. These analytical results align with the numerical solutions of the field equation. Our study covers three spacetime backgrounds: de Sitter, power-law inflation, and the Starobinsky inflation model. Within these models, we identify two distinct phases of particle production: during and after inflation. During inflation, we derive an accurate analytic expression for the particle production rate, accounting for a varying Hubble rate. After inflation, the additional burst of particle production depends on the inflaton mass around its minimum. When this mass is smaller than the Hubble scale during inflation, $H_I$, there is no significant extra production. However, if the inflaton mass is larger, post-inflation production becomes the dominant contribution. Furthermore, we explore the implications of gravitationally produced heavy fields for dark matter abundance, assuming their cosmological stability.