# Frame (In)equivalence in Quantum Field Theory and Cosmology

## TL;DR

This paper investigates how the choice of frame in quantum field theory with gravity affects the path integral measure and quantum effective action, revealing a new 'frame discriminant' term crucial for understanding early Universe models.

## Contribution

It introduces the concept of the frame discriminant, a finite contribution to the effective action arising from measure transformations, impacting the analysis of scalar-tensor theories in cosmology.

## Key findings

- The measure depends non-trivially on fields due to diffeomorphism invariance.
- The frame discriminant influences the dynamics in scalar-tensor theories.
- In the Jordan frame, the discriminant acts as a scale-invariant regularization.

## Abstract

We revisit the question of frame equivalence in Quantum Field Theory in the presence of gravity, a situation of relevance for theories aiming to describe the early Universe dynamics and Inflation in particular. We show that in those cases, the path integral measure must be carefully defined and that the requirement of diffeomorphism invariance forces it to depend non-trivially on the fields. As a consequence, the measure will transform also non-trivially between different frames and it will induce a new finite contribution to the Quantum Effective Action that we name frame discriminant. This new contribution must be taken into account in order to asses the dynamics and physical consequences of a given theory. We apply our result to scalar-tensor theories described in the Einstein and Jordan frame, where we find that the frame discriminant can be thought as inducing a scale-invariant regularization scheme in the Jordan frame.