Cosmological Perturbations and the Physical Meaning of Gaugeinvariant Variables
Abstract
This paper concerns gaugeinvariant perturbations of RobertsonWalker spacetimes, with the aim of (1) giving a complete set of perturbation equations and (2) comparing the coordinatebased method of Bardeen with the covariant approach of Ellis & Bruni. To this end, we first consider covariantly defined quantities which are gaugeinvariant in a perturbed RobertsonWalker 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 secondorder linear equation for the density perturbation variables. Then we systematically expand the covariant and gaugeinvariant variables, recovering Bardeen's variables as firstorder 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. All equations are devised using the hydrodynamic approximation for a fluid with the energy momentum tensor including viscous terms.
 Publication:

The Astrophysical Journal
 Pub Date:
 August 1992
 DOI:
 10.1086/171629
 Bibcode:
 1992ApJ...395...34B
 Keywords:

 Galactic Evolution;
 Gauge Invariance;
 Hydrodynamics;
 Perturbation Theory;
 Relativistic Theory;
 Computational Astrophysics;
 Linear Equations;
 Relic Radiation;
 Astrophysics;
 COSMOLOGY: THEORY;
 GALAXIES: FORMATION;
 HYDRODYNAMICS;
 RELATIVITY