Minimal closed set of observables in the theory of cosmological perturbations. IV. The anisotropic paradigm

Abstract

A. Introductory remarks It has been a common practice ~since Lifshitz’s original paper @1#! to examine the perturbation theory of Einstein’s general relativity by considering variations of nonobservable quantitites such as dgmn . The main drawback of this procedure is that it mixes true perturbations and arbitrary ~infinitesimal! coordinate transformations. We are then faced with an extra task: the separation of true perturbation terms from a mere coordinate transformation. This is the so-called gauge problem of the perturbation theory. A solution for this difficulty was found by many authors ~see Refs. @2‐8#! by looking for gauge-independent combinations which are written in terms of the metric tensor and its derivatives. The next step would then be to provide, from Einstein’s equations that deal with dgmn , the dynamics of these gaugeindependent variables which would then be used to describe physically relevant quantities. We follow a different path. From the beginning, we choose the gauge-invariant physically observable quantities. The dynamics for these fundamental quantities was then analyzed, based on the quasiMaxwellian representation of Einstein’s equations. The method avoids, from the beginning, the problem of gaugedependent variables and any remaining gauge-dependent ob