Cosmological perturbations and the physical meaning of gauge-invariant variables

Details Cosmological perturbations and the physical meaning of gauge-invariant variables Cosmological perturbations and the physical meaning of gauge-invariant variables

Aug 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992apj...395...34b&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 395, no. 1, p. 34-53.

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158

Galactic Evolution, Gauge Invariance, Hydrodynamics, Perturbation Theory, Relativistic Theory, Computational Astrophysics, Linear Equations, Relic Radiation

Scientific paper

This paper concerns gauge-invariant perturbations of Robertson-Walker spacetimes, with the aim of (1) giving a complete set of perturbation equations and (2) comparing the coordinate-based method of Bardeen with the covariant approach of Ellis and Bruni (1989). To this end, we first consider covariantly defined quantities which are gauge-invariant in a perturbed Robertson-Walker universe: for these variables we derive a complete set of covariant linearized equations as they follow from the Bianchi and Ricci identities, and we show various possible ways of obtaining a second-order linear equation for the density perturbation variables. Then we systematically expand the covariant and gauge-invariant variables, recovering Bardeen's variables as first-order terms in this expansion: thus the two sets of variables are equivalent to first order. Through this comparison Bardeen's variables are shown to have a natural physical and geometrical meaning, which can be determined without the need of a gauge specification, and Bardeen's equations follow directly.

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