Tenacious myths about cosmological perturbations larger than the horizon size

Abstract

The linear perturbation theory of the Einstein-de Sitter (k = 0, Friedmann) big-bang cosmology in synchronous gauge is reviewed, with particular care taken to distinguish physical perturbations, which are locally measurable, from pure-gauge perturbations, which correspond to an unperturbed spacetime written in gauge-perturbed coordinates. Some new results are obtained about the growth of physical perturbations at early times, while they are still outside their horizon; and some commonly accepted rules for estimating the growth and decay of perturbations are shown to be false. Source terms corresponding to inhomogeneous perturbations in the equation of state (or, equivalently, to isothermal perturbations) are next included: the density perturbations that are induced are calculated, including both pressure terms and (higher-order) pressure-gradient terms. Here also, some uncritical beliefs are shown to be incorrect.