A note on inflationary scenario with non-minimal coupling

TL;DR

This paper analyzes first-order perturbations in a non-minimally coupled inflationary model, demonstrating that under slow-roll conditions, results align with adiabatic assumptions and previous findings on spectral index and coupling bounds.

Contribution

It shows that non-adiabatic perturbations in non-minimally coupled inflation can be approximated as adiabatic under slow-roll, confirming earlier results with a different approach.

Findings

Spectral index results match previous adiabatic-based calculations.

Bounds on non-minimal coupling parameter are consistent with earlier work.

Perturbation theory simplifies under slow-roll assumptions.

Abstract

We consider first order perturbation theory for a non-minimally coupled inflaton field without assuming an adiabatic equation of state. In general perturbations in non-minimally coupled theory may be non-adiabatic. However under the slow-roll assumptions the perturbation theory may look like adiabatic one. We show in the frame-work of perturbation theory, that our results of spectral index and bound on no-minimal coupling parameter agree with the results obtained using the adiabatic equation of state by the earlier authors.