A study of perturbations in scalar-tensor theory using 1+3 covariant approach

TL;DR

This paper develops a covariant perturbation framework for scalar-tensor gravity theories, especially Brans-Dicke and $f(R)$ models, analyzing density perturbations during different cosmic eras with novel findings on oscillatory behaviors.

Contribution

It introduces a covariant formalism for perturbations in scalar-tensor theories and uncovers new behaviors of radiation perturbations for specific $f(R)$ models.

Findings

Dust perturbations grow exponentially in matter era.

Radiation perturbations oscillate with amplitude growth or decay depending on n.

New results on oscillatory behavior of radiation perturbations for $f(R)$ models.

Abstract

This work discusses scalar-tensor theories of gravity, with a focus on the Brans-Dicke subclass, and one that also takes note of the latter's equivalence with $f(R)$ gravitation theories. A 1+3 covariant formalism is used in this case to discuss covariant perturbations on a background Friedmann-Laimaitre-Robertson-Walker (FLRW) space-time. Linear perturbation equations are developed, based on gauge-invariant gradient variables. Both scalar and harmonic decompositions are applied to obtain second-order equations. These equations can then be used for further analysis of the behavior of the perturbation quantities in such a scalar-tensor theory of gravitation. Energy density perturbations are studied for two systems, namely for a scalar fluid-radiation system and for a scalar fluid-dust system, for $R^{n}$ models. For the matter dominated era, it is shown that the dust energy density perturbations grow exponentially, a result which agrees with those already in existing literature. In the radiation-dominated era, it is found that the behavior of the radiation energy-density perturbations is oscillatory, with growing amplitudes for n>1, and with decaying amplitudes for 0<n<1. This is a new result.