Frame Transformations of Gravitational Theories

TL;DR

This paper develops a method to map gravitational theories from the Jordan frame to the Einstein frame at the quantum level, with applications to models like Higgs inflation, enhancing understanding of quantum effects in curved spacetime.

Contribution

It provides a general procedure for quantum frame transformations applicable to a wide class of gravitational theories, including Higgs inflation.

Findings

Successfully mapped F(φ, R) theories from Jordan to Einstein frame at quantum level

Applied the method to Higgs inflation model

Framework can be extended to other gravitational theories

Abstract

We show how to map gravitational theories formulated in the Jordan frame to the Einstein frame at the quantum field theoretical level considering quantum fields in curved space-time. As an example, we consider gravitational theories in the Jordan frame of the type $F(\phi,\, R)=f(\phi)\, R-V(\phi)$ and perform the map to the Einstein frame. Our results can easily be extended to any gravitational theory. We consider the Higgs inflation model as an application of our results.