Frame (In)equivalence in Quantum Field Theory and Cosmology

Abstract

We revisit the question of frame equivalence in Quantum Field Theory in the presence of gravity, a situation of relevance for theories aiming to describe the early Universe dynamics and Inflation in particular. We show that in those cases, the path integral measure must be carefully defined and that the requirement of diffeomorphism invariance forces it to depend non-trivially on the fields. As a consequence, the measure will transform also non-trivially between different frames and it will induce a new finite contribution to the Quantum Effective Action that we name frame discriminant. This new contribution must be taken into account in order to asses the dynamics and physical consequences of a given theory. We apply our result to scalar-tensor theories described in the Einstein and Jordan frame, where we find that the frame discriminant can be thought as inducing a scale-invariant regularization scheme in the Jordan frame.

arXiv comment33 pages, minor corrections

References in corpus (61)

• f(R) theories
• Cosmology and the Fate of Dilatation Symmetry
• The Standard Model Higgs boson as the inflaton
• Heat kernel expansion: user's manual
• Monodromy in the CMB: Gravity Waves and String Inflation
• Gravity Waves and Linear Inflation from Axion Monodromy
• Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase
• Universality Class in Conformal Inflation
• Higgs inflation: consistency and generalisations
• Hilltop Inflation
• Inflation scenario via the Standard Model Higgs boson and LHC
• On Inflation with Non-minimal Coupling
• Phantom scalar dark energy as modified gravity: understanding the origin of the Big Rip singularity
• Quantum scale invariance, cosmological constant and hierarchy problem
• Scale invariance, unimodular gravity and dark energy
• A review of Axion Inflation in the era of Planck
• Higgs inflation
• Question of quantum equivalence between Jordan frame and Einstein frame
• Local Conformal Symmetry in Physics and Cosmology
• Higgs boson, renormalization group, and naturalness in cosmology
• Equivalence of the Einstein and Jordan frames
• Single-field $\alpha$-attractors
• Physical non-equivalence of the Jordan and Einstein frames
• The renormalization group for non-renormalizable theories: Einstein gravity with a scalar field
• Quantum dilatonic gravity in d = 2,4 and 5 dimensions
• Some aspects of the cosmological conformal equivalence between ``Jordan Frame'' and ``Einstein Frame''
• Higgs-Dilaton Cosmology: an effective field theory approach
• Frame-dependence of higher-order inflationary observables in scalar-tensor theories
• Scale-Independent Inflation and Hierarchy Generation
• Quantum Corrections to Unimodular Gravity
• Correspondence of $F(R)$ Gravity Singularities in Jordan and Einstein Frames
• One-loop divergences for gravity non-minimally coupled to a multiplet of scalar fields: calculation in the Jordan frame. I. The main results
• The Renormalization Group and Weyl-invariance
• Higgs mass naturalness and scale invariance in the UV
• Deceleration versus Acceleration Universe in Different Frames of $F(R)$ Gravity
• Renormalization of gauge theories in the background-field approach
• Manifestly scale-invariant regularization and quantum effective operators
• Inflation in a scale invariant universe
• Inertial Spontaneous Symmetry Breaking and Quantum Scale Invariance
• Spontaneously Broken Conformal Symmetry: Dealing with the Trace Anomaly
• Frame Covariant Nonminimal Multifield Inflation
• Frame-Covariant Formulation of Inflation in Scalar-Curvature Theories
• A question mark on the equivalence of Einstein and Jordan frames
• Higgs-Dilaton Cosmology: An inflation - dark energy connection and forecasts for future galaxy surveys
• Physical renormalization schemes and asymptotic safety in quantum gravity
• Two-loop scale-invariant scalar potential and quantum effective operators
• RG flow of Weyl-invariant dilaton gravity
• Running couplings with a vanishing scale anomaly
• Scale-invariance as the origin of dark radiation?
• Frame-invariant approach to higher-dimensional scalar-tensor gravity
• New Weyl-invariant vector-tensor theory for the cosmological constant
• Unitarity and predictiveness in new Higgs inflation
• Anomalies, equivalence and renormalization of cosmological frames
• Brans-Dicke theory in the local potential approximation
• Affine quantisation of the Brans-Dicke theory: Smooth bouncing and the equivalence between the Einstein and Jordan frames
• Are the String and Einstein Frames Equivalent
• Asymptotic Scale Invariance and its Consequences
• Hidden and explicit quantum scale invariance
• Quantum implications of a scale invariant regularisation
• Gravitational corrections to Higgs potentials
• Conformal and non Conformal Dilaton Gravity

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• Canonical Analysis of Brans-Dicke Theory Addresses Hamiltonian Inequivalence between Jordan and Einstein Frames
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• Towards a unitary, renormalizable and ultraviolet-complete quantum theory of gravity
• The search for the universality class of metric quantum gravity
• Imprints of screened dark energy on nonlocal quantum correlations
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• Jordan and Einstein Frames from the perspective of $\omega =-3/2$ Hamiltonian Brans-Dicke theory
• No-scale Brans-Dicke Gravity -- ultralight scalar boson & heavy inflaton
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• Dynamical dark energy in the no-scale Brans-Dicke gravity
• What can we learn from the conformal noninvariance of the Klein-Gordon equation?
• Ward identities under the frame transformations in curved spacetime