Particle Production after Inflation with Non-minimal Derivative Coupling to Gravity

TL;DR

This paper investigates the post-inflationary universe in models with non-minimal derivative coupling to gravity, analyzing particle and graviton production, and identifying potential instabilities due to oscillating sound speed.

Contribution

It provides a detailed analysis of particle and graviton production in non-minimal derivative coupling models and highlights stability conditions related to sound speed oscillations.

Findings

Particle production rates match Einstein gravity when sound speed squared is positive.

Oscillations in sound speed squared can lead to instabilities.

Graviton production is significantly affected by the non-minimal coupling.

Abstract

We study cosmological evolution after inflation in models with non-minimal derivative coupling to gravity. The background dynamics is solved and particle production associated with rapidly oscillating Hubble parameter is studied in detail. In addition, production of gravitons through the non-minimal derivative coupling with the inflaton is studied. We also find that the sound speed squared of the scalar perturbation oscillates between positive and negative values when the non-minimal derivative coupling dominates over the minimal kinetic term. This may lead to an instability of this model. We point out that the particle production rates are the same as those in the Einstein gravity with the minimal kinetic term, if we require the sound speed squared is positive definite.