Quantum equivalence of $f(R)$ gravity and scalar-tensor theories

TL;DR

This paper examines whether the classical equivalence between $f(R)$ gravity and scalar-tensor theories persists at the quantum level, finding that quantum corrections break the equivalence off-shell but it is restored on-shell.

Contribution

The study provides a detailed comparison of one-loop divergences, revealing the conditions under which quantum equivalence holds or breaks.

Findings

Quantum corrections break off-shell equivalence

On-shell equivalence is restored after quantum corrections

One-loop divergences differ off-shell but agree on-shell

Abstract

We investigate whether the classical equivalence of $f(R)$ gravity and its formulation as scalar-tensor theory still holds at the quantum level. We explicitly compare the corresponding one-loop divergences and find that the equivalence is broken by off-shell quantum corrections, but recovered on-shell.