Herman, David Leigh2013-02-272013-02-272013-02-27http://hdl.handle.net/10222/21376The 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.en-USCosmologyCosmological AveragingDifferential GeometryPerturbation Theory in CosmologyGeneral RelativityThe Gauge IssueThesis