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

Understand

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.