Mathematics – Logic
Scientific paper
Nov 1996
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996gregr..28.1335b&link_type=abstract
General Relativity and Gravitation, Volume 28, Issue 11, pp.1335-1359
Mathematics
Logic
5
Cold Dark Matter
Scientific paper
Beginning from the Einstein-Liouville coupled system of equations for the description of a universe consisting of massive collisionless particles (dark matter), this paper presents a totally gauge-invariant framework for studying the time development of perturbations in homogeneous and isotropic cosmological models. Since the Einstein-Liouville system involves infinitely many degrees of freedom (a function of the momentum variable), emphasis is placed on finding conditions under which the dark mass behaves in an essentially hydrodynamic way. It is demonstrated that, for collisionless matter in the late universe, the complete characterization of cosmological perturbations can be obtained if one defines in a suitable way eighteen “geometrically” independent, not identically vanishing gauge-invariant variables. These basic variables are important because they enable one to divide the infinitesimal perturbations into physically natural equivalence classes: two infinitesimal perturbationsδG 0 andδG {0/'} are said to be equivalent if there is a transformation of the Lie type which carriesδG 0 intoδG {0/'} and vice versa. Another welcome feature of this formulation is that any gauge-invariant quantity can be constructed directly from the basic variables through purely algebraic and differential operations. Comparisons with other work on the Einstein-Liouville system are also made.
Banach Zbigniew
Piekarski Slawomir
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