Average cosmic evolution in a lumpy universe
Degree GrantorUniversity of Canterbury
Degree NameMaster of Science
The procedure of averaging and coarse-graining of the gravitational field equations with sources are investigated in both Newtonian gravity and in general relativity. In particular the schemes of Buchert and Korzyńnski are examined and compared in both situations. In Newtonian gravity it is shown how to calculate the tidal tensor given boundary conditions for it and how to average it given those boundary conditions. It is also shown that one can always choose boundary conditions to make the average tidal tensor vanish or take any value. The problems of coarse-graining tensors in general relativity are critically examined, and a set of relevant conditions for such a procedure are enumerated. Korzyńnski's covariant coarse-graining procedure is reviewed and applied to a particular case. For the case of the Lemaître-Tolman-Bondi model it is shown that the backreaction was always zero for a centred spherical coarse-graining domain. Wiltshire's timescape model, which applies a particular observational interpretation to Buchert's averaging scheme, is reviewed. The dust timescape model of Wiltshire is extended by the addition of a homogeneous radiation source. This model is solved numerically and it is shown not to vary significantly from the dust model since the redshift z ≈ 30, which is when the backreaction and radiation density are equal. The model is integrated back in time from the surface of last scattering with results indicating a breakdown in aspects of the model at early times.