Generalized Slow-roll Inflation in Non-minimally Coupled Theories

TL;DR

This paper develops and compares two methods for deriving slow-roll inflation equations in non-minimally coupled scalar field theories, finding that conformal transformation yields more precise spectral index calculations.

Contribution

It introduces a second method using conformal transformation to derive slow-roll equations in non-minimal coupling, improving accuracy over direct generalization.

Findings

The conformal transformation method provides more precise spectral index calculations.

Comparison shows differences between the two methods in slow-roll inflation modeling.

The paper advances understanding of inflation in non-minimally coupled theories.

Abstract

The slow-roll field equations for the case of non-minimally coupled scalar fields are obtained in two ways: first using the direct generalization of slow-roll conditions in the minimal coupling case to non-minimal one; and, second, conformal transforming the slow-roll field equations in the Einstein frame to the Jordan frame and then applying the generalized slow-roll conditions. We compare the difference of two methods in calculation of the spectral index, $n_s$, for a model example. The second method seems to be more precise.