Invariant slow-roll parameters in scalar-tensor theories

TL;DR

This paper compares slow-roll inflation parameters in scalar-tensor theories across Einstein and Jordan frames using invariant quantities, demonstrating their equivalence up to second order in spectral index calculations.

Contribution

It introduces a framework using invariant quantities to compare slow-roll regimes in different scalar-tensor formulations, clarifying their equivalence.

Findings

Frames are equivalent up to second order in spectral index calculations.

Invariant quantities facilitate comparison across different parametrizations.

The approach confirms the consistency of slow-roll parameters in scalar-tensor theories.

Abstract

A general scalar-tensor theory can be formulated in different parametrizations that are related by a conformal rescaling of the metric and a scalar field redefinition. We compare formulations of slow-roll regimes in the Einstein and Jordan frames using quantities that are invariant under the conformal rescaling of the metric and transform as scalar functions under the reparametrization of the scalar field. By comparing spectral indices, calculated up to second order, we find that the frames are equivalent up to this order, due to the underlying assumptions.