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

TL;DR

This paper investigates how conformal transformations affect cosmological models in modified gravity, revealing significant differences between Einstein and Jordan frames, especially in scalar perturbations and growth rates, using covariant approaches.

Contribution

It provides a detailed covariant analysis of conformal transformations in modified gravity cosmology, highlighting differences between frames and effects on perturbations and cosmological parameters.

Findings

Conformal transformations can change the physical characteristics of cosmological models.

Scalar perturbations are affected by conformal transformations, unlike vector and tensor perturbations.

Differences between Einstein and Jordan frames are significant, especially in growth rates and perturbation behavior.

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.