Integrability conditions of quasi-Newtonian cosmologies in modified gravity

Abstract

We investigate the integrability conditions of a class of shear-free perfect-fluid cosmological models within the framework of anisotropic fluid sources, applying our results to f(R) dark energy models. Generalising earlier general relativistic results for time-like geodesics, we extend the potential and acceleration terms of the quasi-Newtonian formulation of integrable dust cosmological models about a linearized Friedmann-Lemaitre-Robertson-Walker background and derive the equations that describe their dynamical evolutions. We show that in general, models with an anisotropic fluid source are not consistent, but because of the particular form the anisotropic stress takes in f(R) gravity, the general integrability conditions, in this case, are satisfied.

arXiv comment13 pages, no figures

References in corpus (16)

• Extended Theories of Gravity
• Cosmology with Mimetic Matter
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• Linearisation instability of gravity waves?
• Density perturbations with relativistic thermodynamics
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• Imperfect Dark Matter
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• Equations of Gravitational Instability are Non-Local
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• Local freedom in the gravitational field
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• Quasi-Newtonian dust cosmologies
• Shear free solutions in General Relativity Theory
• On Shear-free perturbations of f(R) gravity
• Anti-Newtonian cosmologies in f(R) gravity

Cited by in corpus (5)

• Recovering a MOND-like acceleration law in mimetic gravity
• Reconstructing f(R) Gravity from a Chaplygin Scalar Field in de Sitter Spacetimes
• On 1 + 3 covariant perturbations of the quasi-Newtonian space-time in modified Gauss-Bonnet gravity
• Perturbations of quasi-Newtonian universes in scalar-tensor gravity
• Covariant density and velocity perturbations of the quasi-Newtonian cosmological model in $f(T)$ gravity