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

Riccardo Catena, Massimo Pietroni, and Luca Scarabello
Phys. Rev. D 76, 084039 – Published 31 October 2007

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 cosmic microwave background 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.

  • Received 21 June 2006

DOI:https://doi.org/10.1103/PhysRevD.76.084039

©2007 American Physical Society

Authors & Affiliations

Riccardo Catena

  • Deutsches Elektronen-Syncrotron DESY, 22603 Hamburg, Germany

Massimo Pietroni

  • INFN, Sezione di Padova, via Marzolo 8, I-35131, Padova, Italy

Luca Scarabello

  • Dipartimento di Fisica Università di Padova and INFN, Sezione di Padova, via Marzolo 8, I-35131, Padova, Italy

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Issue

Vol. 76, Iss. 8 — 15 October 2007

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