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arXiv · 1801.01758

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

Joseph Ntahompagaze·Amare Abebe·Manasse R. Mbonye
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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.

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Joseph Ntahompagaze, Amare Abebe, Manasse R. Mbonye. 2018-01-05. A study of perturbations in scalar-tensor theory using 1+3 covariant approach. https://doi.org/10.1142/s0218271818500335

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