1992/08/01 by Marco Bruni, Peter K. S. Dunsby, George Ellis · 11 citations
Physics and Astronomy · Earth and Planetary Sciences · #Cosmology and Gravitation Theories #Solar and Space Plasma Dynamics #Geophysics and Gravity Measurements #Physics #Cosmological perturbation theory #Mathematical physics #Covariant transformation #Cosmology #Perfect fluid #Invariant (physics) #Perturbation theory (quantum mechanics) #Gauge theory #Theoretical physics #Perturbation (astronomy) #Universe #Metric expansion of space #Dark energy #Quantum mechanics
paper · doi:10.1086/171629
openalex publication_date 1992/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02
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 & Bruni. 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. All equations are devised using the hydrodynamic approximation for a fluid with the energy momentum tensor including viscous terms.