Equivalence of the Einstein and Jordan frames

Abstract

No experiment can measure an absolute scale: every dimensionfull quantity has to be compared to some fixed unit scale in order to be measured, and thus only dimensionless quantities are really physical. The Einstein and Jordan frame are related by a conformal transformation of the metric, which amounts to rescaling all length scales. Since the absolute scale cannot be measured, both frames describe the same physics, and are equivalent. In this article we make this explicit by rewriting the action in terms of dimensionless variables, which are invariant under a conformal transformation. For definiteness, we concentrate on the action of Higgs inflation, but the results can easily be generalized. In addition, we show that the action for f(R)-gravity, which includes Starobinsky inflation, can be written in a frame-independent form.

published version

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• Frame Covariant Nonminimal Multifield Inflation
• Unimodular $f(R,T)$ Gravity
• Critical point Higgs inflation in the Palatini formulation
• Analytic Solution of the Starobinsky Model for Inflation
• Equivalence of cosmological observables in conformally related scalar tensor theories
• Minimal plateau inflationary cosmologies and constraints from reheating
• Post-Newtonian parameters $\gamma$ and $\beta$ of scalar-tensor gravity for a homogeneous gravitating sphere
• Do metric fluctuations affect the Higgs dynamics during inflation?
• On the Cosmological Frame Problem
• Mimetic gravity: mimicking the dynamics of the primeval universe in the context of loop quantum cosmology
• Hyperbolic inflation in the Jordan frame
• Top-Goldstone coupling spoils renormalization of Higgs inflation
• Aspects of Quantum Cosmology