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

Riccardo Catena

Massimo Pietroni

Luca Scarabello

  • Deutsches Elektronen-Syncrotron DESY, 22603 Hamburg, Germany

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

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

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Phys. Rev. D 76, 084039 – Published 31 October, 2007

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

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.

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Phys. Rev. D 76, 084039– Published 31 October, 2007
  • Received 21 June 2006

© 2007 American Physical Society

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