Extended Slow-Roll Conditions and Rapid-Roll Conditions

TL;DR

This paper derives and compares slow-roll and rapid-roll conditions for a non-minimally coupled scalar field, providing spectral index expressions and proving conformal invariance without linear approximations.

Contribution

It introduces consistent slow-roll and rapid-roll conditions for non-minimally coupled scalar fields and proves conformal invariance of curvature perturbations without linear approximations.

Findings

Spectral indices expressed in terms of slow-roll parameters

Conformal invariance of curvature perturbation proved without linear approximation

Relations between rapid-roll and slow-roll conditions established

Abstract

We derive slow-roll conditions for a scalar field which is non-minimally coupled with gravity in a consistent manner and express spectral indices of scalar/tensor perturbations in terms of the slow-roll parameters. The conformal invariance of the curvature perturbation is proved without linear approximations. Rapid-roll conditions are also derived, and the relation with the slow-roll conditions is discussed.