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

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.

7 pages, 1 figure; references added, accepted for publication in Phys. Rev. D

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Cited by in corpus (59)

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• Primordial black hole dark matter in dilaton-extended two-field Starobinsky inflation
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• On the equivalence between Starobinsky and Higgs inflationary models in gravity and supergravity
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• Non-minimal (self-)running inflation: metric vs. Palatini formulation
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• Inflation with $R_{(\alpha \beta )}$ terms in the Palatini formulation
• Dynamical equivalence of $f(R)$ gravity in Jordan and Einstein frames
• One-loop renormalization in Galileon effective field theory
• Extended phase space thermodynamics of black holes: A study in Einstein's gravity and beyond
• On the equivalence of Jordan and Einstein frames in scale-invariant gravity
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• Generalized Ashtekar variables for Palatini f(R) models
• Geometrized quantum Galileons
• Unification of inflation and dark matter in the Higgs-Starobinsky model
• Bounce from Inflation
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• Fluid-gravity correspondence in the scalar-tensor theory of gravity: (in)equivalence of Einstein and Jordan frames
• Thermodynamic structure of a generic null surface and the zeroth law in scalar-tensor theory
• Formalizing Slow-roll Inflation in Scalar-Tensor Theories of Gravitation
• Renormalizability of alternative theories of gravity: differences between power counting and entropy argument
• Attractor Cosmology from non-minimally Coupled Gravity
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• Ultraviolet Unitarity Violations in Non-minimally Coupled Scalar-Starobinsky Inflation
• Renormalization Group for Non-minimal ${\varphi }^{2}R$ Couplings and Gravitational Contact Interactions
• A note on the linear stability of black holes in quadratic gravity
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• Conformal and kinetic couplings as two Jordan frames of the same theory
• Naked singularities in quadratic f(R) gravity
• Jordan and Einstein Frames from the perspective of $\omega =-3/2$ Hamiltonian Brans-Dicke theory
• Scalar-tensor gravity from thermodynamic and fluid-gravity perspective
• An issue with the classification of the scalar-tensor theories of gravity
• Non-perturbative quantum Galileon in the exact renormalization group
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• Scalar fluid in scalar-tensor gravity from an equivalent picture of thermodynamic and fluid descriptions of gravitational dynamics
• Equivalence of scalar-tensor theories and scale-dependent gravity
• Scalar-tensor theories of gravity from a thermodynamic viewpoint
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• Starobinksy Inflation, Gravitational Contact Terms and the Induced BEH Boson Mass
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