$f(R, R_{\mu\nu}^2)$ at one loop

TL;DR

This paper calculates one-loop divergences in a generalized gravity theory with a complex Lagrangian, revealing invariance under duality transformations and equivalence with unimodular gravity at one-loop order.

Contribution

It provides the first detailed computation of one-loop divergences for $f(R,R_{ ext{μν}}^2)$ gravity and explores duality invariance and unimodular equivalence.

Findings

One-loop divergences are explicitly computed for the general $f(R,R_{ ext{μν}}^2)$ theory.

The one-loop effective action remains invariant under a specific duality transformation.

Unimodular gravity is shown to be equivalent to the general theory at one-loop order.

Abstract

We compute the one-loop divergences in a theory of gravity with Lagrangian of the general form $f(R,R_{\mu\nu}R^{\mu\nu})$, on an Einstein background. We also establish that the one-loop effective action is invariant under a duality that consists of changing certain parameters in the relation between the metric and the quantum fluctuation field. Finally, we discuss the unimodular version of such a theory and establish its equivalence at one-loop order with the general case.