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

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.

14 pages, v2:minor corrections, refs. added/modified

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Cited by in corpus (12)

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• Asymptotic safety and field parametrization dependence in the f(R) truncation
• On the impact of Majorana masses in gravity-matter systems
• Can quantum fluctuations differentiate between standard and unimodular gravity?
• Exploring new corners of asymptotically safe unimodular quantum gravity
• Nonlinear Evolution of Quadratic Gravity in 3+1 Dimensions
• $f\left(R,{\nabla }_{{\mu }_1}R,\dots ,{\nabla }_{{\mu }_1}\dots {\nabla }_{{\mu }_n}R\right)$ theories of gravity in Einstein frame: A higher order modified Starobinsky inflation model in the Palatini approach
• Vilkovisky unique effective action in quantum gravity
• On characterizing the Quantum Geometry underlying Asymptotic Safety
• Modified gravity one-loop partition function
• Coarse-graining of the Einstein-Hilbert Action rewritten by the Fisher information metric
• Cosmology in the mimetic higher-curvature $f(R,R_{\mu \nu }{R}^{\mu \nu })$ gravity