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Volume-Preserving Coordinate Gauges in Linear Perturbation Theory

Date

2013-02-27

Authors

Herman, David Leigh

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Abstract

The main goal of this thesis is to present cosmological perturbation theory (based on the standard Friedmann cosmological model) in volume-preserving coordinates, which then provides a suitable basis for studies in cosmological averaging. We review perturbation theory to second order, allowing for averaging to second order in future research. To solve the averaging problem we need a method of covariantly and gauge invariantly averaging tensorial objects on a background manifold. This is a very difficult problem. However, the definition of an average takes on a particularly simple form when written in a system of volume-preserving coordinates. Therefore, we develop a three dimensional and a four dimensional volume-preserving coordinate gauge in this thesis that can be used for averaging in cosmological perturbation theory.

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Keywords

Cosmology, Cosmological Averaging, Differential Geometry, Perturbation Theory in Cosmology, General Relativity, The Gauge Issue

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