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.
Highlights
The calculation of the one-loop divergences in Einstein theory without cosmological constant was performed originally in [1] and established the perturbative nonrenormalizability of the theory in the presence of matter
In a context of asymptotic safety, these beta functions were reproduced starting from the functional renormalization group in [9,10] and in other dimensions in [11], and pushed beyond the one-loop approximation in [12,13,14]
We found in [53,54] that the divergences of Einstein theory and of higher-derivative gravity on an Einstein background are invariant under the following change of the parameters: ðω; mÞ
Summary
The calculation of the one-loop divergences in Einstein theory without cosmological constant was performed originally in [1] and established the perturbative nonrenormalizability of the theory in the presence of matter. The one-loop divergences for such a theory, on a maximally symmetric background, have been computed originally in [29] This calculation has been extended recently to arbitrary backgrounds [30] and to Einstein spaces [31]. We have computed the gauge and parametrization dependence of the one-loop divergences in Einstein gravity [53] and higher-derivative gravity [54] (with four free parameters altogether). We will use this general parametrization in this paper.
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