Gauge invariant perturbation theory in spatially homogeneous cosmology
Abstract
The perturbations of the L.R.S. class A spatially homogeneous spacetimes are treated using Hamiltonian methods in conjunction with techniques from the theory of Lie group harmonic analysis. These latter techniques lead to a simple way of handling any set of tensor equations on these background spacetimes which has the same symmetry group as the spacetime metric. The Hamiltonian formulation is used to recover in a clean way the Bonanos equations for the perturbations of the perfect fluid models of the class of spacetimes under consideration. The conserved quantities associated with the fourdimensional symmetry group are evaluated and their role in the linearized Hamiltonian dynamics is discussed. The timedependent linear canonical transformation of the linearized vacuum gravitational phase space adapted to Moncrief's gauge invariant decomposition is described in general for these models and evaluated explicitly for a class of lower dimensional harmonic modes.
 Publication:

Ph.D. Thesis
 Pub Date:
 1978
 Bibcode:
 1978PhDT.........5J
 Keywords:

 Cosmology;
 Gauge Invariance;
 Homogeneity;
 Perturbation Theory;
 Hamiltonian Functions;
 Harmonic Analysis;
 Lie Groups;
 Linearization;
 SpaceTime Functions;
 Astrophysics