General Relativity and Gravitation

, Volume 42, Issue 7, pp 1667–1705 | Cite as

Conformal transformations in cosmology of modified gravity: the covariant approach perspective

Research Article
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Abstract

The 1+3 covariant approach and the covariant gauge-invariant approach to perturbations are used to analyze in depth conformal transformations in cosmology. Such techniques allow us to obtain insights on the physical meaning of these transformations when applied to non-standard gravity. The results obtained lead to a number of general conclusions on the change of some key quantities describing any two conformally related cosmological models. For example, even if some of the geometrical properties of the cosmology are preserved (homogeneous and isotropic Universes are mapped into homogeneous and isotropic universes), it can happen that decelerating cosmologies can be mapped into accelerated ones. From the point of view of the cosmological perturbations it is shown how these fluctuation transform. We find that first-order vector and tensor perturbations equations are left unchanged in their structure by the conformal transformation, but this cannot be said of the scalar perturbations, which present differences in their evolutionary features. The results obtained are then explicitly interpreted and verified with the help of some clarifying examples based on f(R)-gravity cosmologies.

Keywords

Conformal transformations Modified gravity Cosmology 1+3 Covariant approach Covariant gauge invariant theory of perturbations 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Sante Carloni
    • 1
  • Emilio Elizalde
    • 2
  • Sergei Odintsov
    • 2
    • 3
  1. 1.Facultat CiènciesInstitut d’Estudis Espacials de Catalunya (IEEC)Bellaterra (Barcelona)Spain
  2. 2.Facultat CiènciesConsejo Superior de Investigaciones Científicas (ICE/CSIC), Institut d’Estudis Espacials de Catalunya (IEEC)Bellaterra (Barcelona)Spain
  3. 3.ICE (CSIC-IEEC), Campus UAB, Facultat CiènciesBellaterra (Barcelona)Spain

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