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-Lemaître-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 π ab takes in f (R) gravity, the general integrability conditions in this case are satisfied.

Reconstructing f(R) gravity from a Chaplygin scalar field in de Sitter spacetimes

“…Among the earliest and simplest modifications to the GR gravitational action are f (R) gravity models. These models are usually considered to be geometrical alternatives to the dark energy debate [22][23][24][25][26][27][28][29][30], but their scopes of applicability has only been increasing: from early-universe cosmic inflation [2,31,32], to the evolutionary dynamics of large-scale structure [33][34][35][36][37][38][39][40][41] and astrophysics [42][43][44][45].…”

Quasi-Newtonian Cosmological Models in Scalar-Tensor Theories of Gravity

“…Newtonian cosmologies are an extension of the Newtonian theory of gravity and are usually referred to as quasi-Newtonian, rather than strictly Newtonian formulations [1,2,3]. The importance of investigating the Newtonian limit for general relativity on cosmological contexts is that, there is a viewpoint that cosmological studies can be done using Newtonian physics, with the relativistic theory only needed for examination of some observational relations [1].…”

“…Given a choice of 4-velocity field u a in the Ehlers-Ellis covariant approach [11,12], the dynamics, kinematics and gravitoelectromagnetics of the FLRW background is characterised respectively by the equations [2,3] …”

“…In other words, it is a non-relativistic peculiar velocity. Quasi-Newtonian cosmological models are irrotational, shear-free dust spacetimes characterised by [2,3]:…”

“…It has been shown [13] that the non-linear models are generally inconsistent if the silent constraint 30 is imposed, but that the linear models are consistent [2,3]. Thus, a simple approach to the integrability conditions for quasi-Newtonian LHEP 01, 21, 2018 cosmologies follows from showing that these models are in fact a sub-class of the linearised silent models.…”