AN ALMOST-ROBERTSON-WALKER UNIVERSE MODEL AND THE EQUIVALENCE CLASSESOF PERTURBATIONS - NONBAROTROPIC PERFECT FLUIDS

A new covariant and gauge-invariant treatment of perturbations, which is applicable to the case of an almost-Robertson-Walker universe domin ated by a general perfect fluid with two essential thermodynamic varia bles, is presented. Beginning from the geometrical foundation, this pa per proposes to define gauge-invariant perturbations as the equivalenc e classes of tangents to one-parameter families of exact solutions of the nonlinear field equations: two tangents delta G(0) and delta G'(0) are said to be equivalent if there is a transformation of the Lie typ e which carries delta G(0) into delta G'(0) and vice-versa. Denoting b y [delta G(0)] the equivalence class of delta G(0), it is demonstrated explicitly in the context of an almost-Robertson-Walker universe mode l that, for nonbarotropic perfect fluids, the precise definition of [d elta G(0)] is equivalent to defining and solving an appropriate system of linear propagation equations for the basic set of variables. This set consists of seventeen linearly independent, not identically vanish ing gauge-invariant and covariantly defined quantities. A simple examp le illustrating the above result is given and elementary comparisons w ith other covariant and gauge-invariant approaches are also made. Fina lly, the paper discusses several new features associated with the so-c alled scalar perturbation theory.