Covariant velocity and density perturbations in quasi-Newtonian cosmologies - art. no. 124006

Recently a covariant approach to cold matter universes in the zero-shear hy persurfaces (or longitudinal) gauge has been developed. This approach revea ls the existence of an integrability condition, which does not appear in st andard non-covariant treatments. A simple derivation and generalization of the integrability condition is given, based on showing that the quasi-Newto nian models are a sub-class of the linearized ''silent'' models. The soluti on of the integrability condition implies a propagation equation for the ac celeration. It is shown how the velocity and density perturbations an then obtained via this propagation equation. The density perturbations acquire a small relative-velocity correction on all scales, arising from the fully c ovariant general relativistic analysis. [S0556-2821(98)04622-0].