Conformal Transformations in Cosmology of Modified Gravity: the Covariant Approach Perspective

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 very interesting insights on the physical content 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. In particular, it is shown that the physics in the Einstein frame has characteristics which are completely different from those in the Jordan frame. 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 are mapped into accelerated ones. Differences become even more pronounced when first-order perturbations are considered: from the 1+3 equations it is seen that first-order vector and tensor perturbations are left unchanged in their structure by the conformal transformation, but this cannot be said of the scalar perturbations, which include the matter density fluctuations. Behavior in the two frames of the growth rate, as well as other evolutionary features, like the presence or absence of oscillations, etc., appear to be different too. The results obtained are then explicitly interpreted and verified with the help of some clarifying examples based on $f(R)$-gravity cosmologies.

26 pages, 8 figures

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• Hawking-Hayward quasi-local energy under conformal transformations
• Deep connection between f(R) gravity and the interacting dark sector model
• Cosmological perturbations in $F(R)$ gravity
• Cosmological perturbations in f(G) gravity
• Revisiting the matter power spectra in $f(R)$ gravity
• A study of perturbations in scalar-tensor theory using 1+3 covariant approach
• On multifluid perturbations in scalar-tensor cosmology
• A new approach to cosmological perturbations in f(R) models
• Cosmological Perturbations and Quasi-Static Assumption in $f(R)$ Theories
• Multifluid cosmology in f (G) gravity
• Reconstruction of f(R) gravity models from observations
• The 1+1+2 formalism for Scalar-Tensor gravity
• Testing gravity with non-Gaussianity
• Gauge Issues in Extended Gravity and f(R) Cosmology
• Jordan and Einstein Frames from the perspective of $\omega =-3/2$ Hamiltonian Brans-Dicke theory
• Reconstructing exact scalar-tensor cosmologies via conformal transformations
• Dynamical system analysis in multiscalar-torsion cosmology
• Hyperbolic inflation in the Jordan frame
• Perturbations of quasi-Newtonian universes in scalar-tensor gravity
• Covariant density and velocity perturbations of the quasi-Newtonian cosmological model in $f(T)$ gravity