GAUGE-INVARIANT PERFECT-FLUID ROBERTSON-WALKER PERTURBATIONS

In the preceding paper, a complete set of basic gauge-invariant variab les was defined that uniquely characterizes cosmological perturbations in homogeneous, isotropic, ideal-fluid universe models. The calculati ons were presented in some detail for the case of a general perfect fl uid with two essential thermodynamic variables. Among other things, it was demonstrated that the aforementioned set consists of 17 linearly independent, not identically vanishing gauge-invariant variables. One can think of these basic variables as having two aspects. First, their definitions are such that they provide a unique representation of the physical perturbation. (By way of digression, inspection shows that s uch perturbations can be regarded as being the elements of a certain q uotient space.) Second, any complicated gauge-invariant quantity is ob tainable directly from the basic variables through purely algebraic an d differential operations. The object here is the systematic derivatio n of the linear propagation equations governing the evolution of these basic variables. To make clear the relation of the present formalism to a series of standard results in the literature, this paper also poi nts out how general propagation equations can be adapted to situations where the pressure vanishes in the background. Finally, the physical interpretation of basic variables and comparison with other gauge-inva riant approaches are briefly presented.