Anomalies, equivalence and renormalization of cosmological frames

Abstract

We study the question of whether two frames of a given physical theory are equivalent or not in the presence of quantum corrections. By using field theory arguments we claim that equivalence is broken in the presence of anomalous symmetries in one of the frames. This is particularized to the case of the relation between the Einstein and Jordan frames in scalar-tensor theories used to describe early Universe dynamics. Although in this case a regularization that cancels the anomaly exists, the renormalized theory always develop a non-vanishing contribution to the S-matrix that is present only in the Jordan frame, promoting the different frames to different physical theories that must be UV completed in a different way.

15 pages, matches the journal version

References in corpus (5)

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• Higgs inflation: consistency and generalisations
• Quantum cosmological consistency condition for inflation
• Conformal and non Conformal Dilaton Gravity
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• Quantum equivalence of $f(R)$ gravity and scalar-tensor theories
• Equivalence of inflationary models between the metric and Palatini formulation of scalar-tensor theories
• Transformations between Jordan and Einstein frames: Bounces, antigravity, and crossing singularities
• Frame-invariant approach to higher-dimensional scalar-tensor gravity
• Essential renormalisation group
• Frame Covariance in Quantum Gravity
• Frame (In)equivalence in Quantum Field Theory and Cosmology
• Jordan frame no-hair for spherical scalar-tensor black holes
• Critical point Higgs inflation in the Palatini formulation
• Tree-level unitarity in Higgs inflation in the metric and the Palatini formulation
• Higgs field in cosmology
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• Induced Gravity and Quantum Cosmology
• Fifth forces and frame invariance
• Ward identities under the frame transformations in curved spacetime