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

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.

4 figures, published in International Journal of Modern Physics D

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Cited by in corpus (9)

• Selected topics in scalar-tensor theories and beyond
• Structure growth in $f(Q)$ cosmology
• Cosmological perturbations in f(G) gravity
• On multifluid perturbations in scalar-tensor cosmology
• The cosmology of $f(R,L_m)$ gravity: constraining the background and perturbed dynamics
• Multifluid cosmology in f (G) gravity
• Constraining viscous fluid models in $f(Q)$ gravity with data
• On 1 + 3 covariant perturbations of the quasi-Newtonian space-time in modified Gauss-Bonnet gravity
• Perturbations with bulk viscosity in modified chaplygin gas cosmology