Gauge invariant cosmological perturbations for the nonminimally coupled inflaton field

TL;DR

This paper develops a gauge invariant formalism for cosmological perturbations in nonminimally coupled inflation models, demonstrating frame equivalence and extending to complex scalar sectors, advancing theoretical understanding of early universe models.

Contribution

It introduces a gauge invariant action formalism for nonminimally coupled inflaton perturbations and generalizes to models with internal scalar symmetries.

Findings

Demonstrates physical equivalence between Jordan and Einstein frames at quadratic level.

Provides a gauge invariant perturbation framework for nonminimal inflation.

Extends formalism to scalar sectors with internal symmetries like Higgs inflation.

Abstract

We construct the gauge invariant free action for cosmological perturbations for the nonminimally coupled inflaton field in the Jordan frame. For this the phase space formalism is used, which keeps track of all the dynamical and constraint fields. We perform explicit conformal transformations to demonstrate the physical equivalence between the Jordan and Einstein frames at the level of quadratic perturbations. We show how to generalize the formalism to the case of a more complicated scalar sector with an internal symmetry, such as Higgs inflation. This work represents a first step in developing gauge invariant perturbation theory for nonminimally coupled inflationary models.