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.

11 pages Revtex; to appear Phys. Rev. D

References in corpus (3)

• Covariant Analysis of Gravitational Waves in a Cosmological Context
• A covariant and gauge-invariant analysis of cosmic microwave background anisotropies from scalar perturbations
• Newtonian-like and anti-Newtonian universes

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