Question of quantum equivalence between Jordan frame and Einstein frame

TL;DR

This paper investigates whether the classical equivalence between Jordan and Einstein frames in scalar-tensor theories persists at the quantum level, finding that off-shell divergences differ but on-shell equivalence is maintained through cancellation.

Contribution

It provides the first explicit calculation of one-loop divergences in both frames and demonstrates on-shell equivalence in a cosmological background.

Findings

Off-shell quantum divergences differ between frames.

On-shell divergences coincide due to cancellation.

Quantum corrections induce off-shell dependence on parametrization.

Abstract

In the framework of a general scalar-tensor theory, we investigate the equivalence between two different parametrizations of fields that are commonly used in cosmology - the so-called Jordan frame and Einstein frame. While it is clear that both parametrizations are mathematically equivalent at the level of the classical action, the question about their mathematical equivalence at the quantum level as well as their physical equivalence is still a matter of debate in cosmology. We analyze whether the mathematical equivalence still holds when the first quantum corrections are taken into account. We explicitly calculate the one-loop divergences in both parametrizations by using the generalized Schwinger-DeWitt algorithm and compare both results. We find that the quantum corrections do not coincide off shell and hence induce an off shell dependence on the parametrization. According to the equivalence theorem, the one-loop divergences should however coincide on shell. For a cosmological background, we show explicitly that the on shell equivalence is indeed realized by a nontrivial cancellation.