GEOMETRIZATION OF LINEAR PERTURBATION-THEORY FOR DIFFEOMORPHISM-INVARIANT COVARIANT FIELD-EQUATIONS .2. BASIC GAUGE-INVARIANT VARIABLES WITH APPLICATIONS TO DE SITTER SPACE-TIME

In a companion paper, a systematic treatment of linearized perturbatio ns and a new geometric definition of gauge-invariant variables, based on the theory of vector bundles and applicable to the case of an arbit rary system of covariant field equations, were carefully presented. On e of the purposes of the present paper is to specify a necessary and s ufficient condition that a given, finite set of gauge-invariant variab les, denoted collectively by omega and referred to as the complete set of basic variables, can be used to extract the equivalence classes of perturbations from omega in a unique way. The above set is complete b ecause it has the following property: a knowledge of omega is all one needs in the sense that if x represents an arbitrary point of the ''sp ace-time'' manifold X and G denotes any gauge-invariant tensor field o n X, then the value of G at x is an element of X is uniquely specified by giving the germs of basic gauge-invariant variables at x is an ele ment of X. Arguments are proposed that omega also has a stronger prope rty which is more immediately useful: any G is obtainable directly fro m the basic variables through purely algebraic and differential operat ions. These results are of practical interest, and one concrete settin g where one is led to the explicit definition of omega occurs when con sidering the infinitesimal perturbation of the metric tensor itself(pu re gravity) defined on a fixed background de Sitter space-time and obe ying the linearized empty-space Einstein equations with nonnegative co smological constant Lambda; the case Lambda = 0 corresponds to linear perturbation theory in Minkowski space-time.