Derivative couplings in gravitational production in the early universe

TL;DR

This paper investigates how derivative couplings to curvature in the early universe influence gravitational particle production, revealing that these couplings significantly alter production rates during inflation and reheating phases.

Contribution

It introduces the most general first order action with derivative couplings to curvature, analyzing their impact on particle production in different cosmological regimes.

Findings

Density of produced particles is constant during de Sitter inflation with derivative couplings.

Derivative couplings to curvature scalar and Ricci tensor have drastically different effects at large masses.

Production rates are highly sensitive to the curvature scalar coupling in the reheating phase.

Abstract

Gravitational particle production in the early universe is due to the coupling of matter fields to curvature. This coupling may include derivative terms that modify the kinetic term. The most general first order action contains derivative couplings to the curvature scalar and to the traceless Ricci tensor, which can be dominant in the case of (pseudo-)Nambu-Goldstone bosons or disformal scalars, such as branons. In the presence of these derivative couplings, the density of produced particles for the adiabatic regime in the de Sitter phase (which mimics inflation) is constant in time and decays with the inverse effective mass (which in turn depends on the coupling to the curvature scalar). In the reheating phase following inflation, the presence of derivative couplings to the background curvature modifies in a nontrivial way the gravitational production even in the perturbative regime. We also show that the two couplings -- to the curvature scalar and to the traceless Ricci tensor -- are drastically different, specially for large masses. In this regime, the production becomes highly sensitive to the former coupling while it becomes independent of the latter.