Physics
Scientific paper
Mar 1996
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996ijtp...35..633b&link_type=abstract
International Journal of Theoretical Physics, Volume 35, Issue 3, pp.633-663
Physics
5
Scientific paper
An annoying paradox which has plagued the “naive” description of density perturbations in homogeneous and isotropic cosmological models has been the gauge-dependent character of this description. The corollary of this observation is that only gauge-invariant quantities have any inherent physical meaning. Thus the present paper develops, from a new geometric point of view, a totally gauge-invariant formulation of perturbation theory applicable to the case of a general perfect fluid with two essential thermodynamic variables. Precisely speaking, the main purpose here is the systematic construction of a complete set of basic gauge-invariant variables. This set consists of 17 linearly independent, not identically vanishing quantities. It turns out that these quantities can be used to divide the infinitesimal perturbations into equivalence classes: two perturbations P and P' are said to be equivalent if their difference is equal to the Lie derivative of the background solution of Einstein's propagation equations with respect to an arbitrary vector field on the space-time manifold. In fact, the gauge-invariant perturbations, whose mathematical definition is best understood by introducing the elements of a certain quotient space, are uniquely determined from the basic variables. An additional welcome feature is that any gauge-invariant quantity can be constructed directly from the basic variables through purely algebraic and differential operations. In a companion paper, these results are used to derive the full, gauge-invariant system of equations governing the evolution of basic variables. In this sense, then, the present analysis is complete.
Banach Zbigniew
Piekarski Sławomir
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