Frame Transformations of Gravitational Theories

Abstract

We show how to map gravitational theories formulated in the Jordan frame to the Einstein frame at the quantum field theoretical level considering quantum fields in curved space-time. As an example, we consider gravitational theories in the Jordan frame of the type $F(\varphi ,R)=f(\varphi )R-V(\varphi )$ and perform the map to the Einstein frame. Our results can easily be extended to any gravitational theory. We consider the Higgs inflation model as an application of our results.

13 pages

References in corpus (3)

• f(R) theories
• The Standard Model Higgs boson as the inflaton
• The dynamical equivalence of modified gravity revisited

Cited by in corpus (23)

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• Higgs Starobinsky Inflation
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• Higgs inflation at the hilltop
• Quantum equivalence of $f(R)$ gravity and scalar-tensor theories
• Transformations between Jordan and Einstein frames: Bounces, antigravity, and crossing singularities
• Palatini frames in scalar-tensor theories of gravity
• Quantum Equivalence of $f(R)$ Gravity and Scalar-tensor Theories in the Jordan and Einstein Frames
• Critical point Higgs inflation in the Palatini formulation
• Duality between static spherically or hyperbolically symmetric solutions and cosmological solutions in scalar-tensor gravity
• Tree-level unitarity in Higgs inflation in the metric and the Palatini formulation
• What is modified gravity and how to differentiate it from particle dark matter?
• New class of hybrid metric-Palatini scalar-tensor theories of gravity
• Do metric fluctuations affect the Higgs dynamics during inflation?
• Higgs field in cosmology
• Invariant quantities of Scalar-Tensor Theories for stellar structure
• Scalar-tensor black holes in an expanding universe
• Induced Gravity and Quantum Cosmology
• Singularity theorems in the effective field theory for quantum gravity at second order in curvature
• Gravitational relaxation of electroweak hierarchy problem
• Scalar-tensor cosmologies in a minisuperspace formulation: a case study