Einstein and Jordan frames reconciled: a frame-invariant approach to scalar-tensor cosmology

Abstract

Scalar-Tensor theories of gravity can be formulated in different frames, most notably, the Einstein and the Jordan one. While some debate still persists in the literature on the physical status of the different frames, a frame transformation in Scalar-Tensor theories amounts to a local redefinition of the metric, and then should not affect physical results. We analyze the issue in a cosmological context. In particular, we define all the relevant observables (redshift, distances, cross-sections, ...) in terms of frame-independent quantities. Then, we give a frame-independent formulation of the Boltzmann equation, and outline its use in relevant examples such as particle freeze-out and the evolution of the CMB photon distribution function. Finally, we derive the gravitational equations for the frame-independent quantities at first order in perturbation theory. From a practical point of view, the present approach allows the simultaneous implementation of the good aspects of the two frames in a clear and straightforward way.

15 pages, matches version to be published on Phys. Rev. D

References in corpus (20)

• A Line of Sight Approach to Cosmic Microwave Background Anisotropies
• Cosmological Perturbation Theory in the Synchronous and Conformal Newtonian Gauges
• Cosmological Perturbation Theory in the Synchronous vs. Conformal Newtonian Gauge
• The String Dilaton and a Least Coupling Principle
• Scalar-tensor gravity in an accelerating universe
• Weak Lensing and Cosmology
• The conformal frame freedom in theories of gravitation
• Scalar-Tensor Gravity and Quintessence
• Cosmic Microwave Background Polarization
• Dark Energy Condensation
• Weak lensing in scalar-tensor theories of gravity
• Dark Matter Relic Abundance and Scalar-Tensor Dark Energy
• Big bang nucleosynthesis constraints on scalar-tensor theories of gravity
• Testing for w<-1 in the Solar System
• Weak lensing in generalized gravity theories
• Predictions and Observations in Theories with Varying Couplings
• Non-linear perturbations in scalar-tensor cosmologies
• Non-linear gravitational clustering in scalar field cosmologies
• Dynamical Relaxation of the Dark Matter to Baryon Ratio
• Local transformations of units in Scalar-Tensor Cosmology

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