Covariant velocity and density perturbations in quasi-Newtonian cosmologies

Abstract

Recently a covariant approach to cold matter universes in the zero-shear hypersurfaces (or longitudinal) gauge has been developed. This approach reveals the existence of an integrability condition, which does not appear in standard non-covariant treatments. A simple derivation and generalization of the integrability condition is given, based on showing that the quasi-Newtonian models are a sub-class of the linearized 'silent' models. The solution of the integrability condition implies a propagation equation for the acceleration. It is shown how the velocity and density perturbations are then obtained via this propagation equation. The density perturbations acquire a small relative-velocity correction on all scales, arising from the fully covariant general relativistic analysis.

General relativistic analysis of peculiar velocities

“…Also to linear order in v a we have π ab = 0. (These linear results are obtained from the exact boost transformation laws (B7) -(B10) given in [16].) In addition, it transforms the kinematic quantities to linear order in v a as follows (cf.…”

“…The gravito-electric/-magnetic Weyl curvature fields are frame-invariant to linear order in v a (cf. the exact boost transformation laws (B11) and (B12) in [16]):…”

“…In addition, it transforms the kinematic quantities to linear order in v a as follows (cf. the exact boost transformation laws (B3) -(B6) in [16]):…”

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].…”

“…Higher-order or modified gravitational theories of gravity such as f (R) theories of gravity have been shown to exhibit more shared properties with Newtonian gravitation than does general relativity [4,5]. In [1], a covariant approach to cold matter universes in quasi-Newtonian cosmologies has been developed and it has been applied and extended in [2] in order to derive and solve the equations governing density and velocity perturbations. This approach revealed the existence of integrability conditions in GR.…”