## 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.

Original language | English |
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Article number | 124006 |

Pages (from-to) | 124006 |

Journal | Physical Review D |

Volume | 58 |

Issue number | 12 |

Publication status | Published - 15 Dec 1998 |