Exact, Inhomogeneous Solutions to Gravitational Theories in Cosmology
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Solving the backreaction and averaging problems is important as we enter the era of precision cosmology. Fundamentally, the idea that small-scale inhomogeneities can a ect the large-scale dynamics of the Universe lies in the non-linearity and non-commutativity properties of the Einstein eld equations. It is not necessarily the case that the dynamics of a perfectly homogeneous Friedmann universe are the same as an inhomogeneous one. However, di culties arise in nding suitable inhomogeneous solutions to the Einstein eld equations. Progress can be made by treating it as an initial data problem and solving the constraint equations. This gives rise to a family of solutions, the black hole lattices, which consist of linearly superposed Schwarzschild masses representing a universe with a discretised matter content. In this thesis, we present extensions and generalisations of these existing models. Firstly, we devised a novel way to include structure formation and its e ects. We did this in a quasi-static approach that involved splitting the black holes up into more masses and moving them along parameterised trajectories. For small values of this parameter, we could induce clustering as the black holes were su ciently close together. We found an extra apparent horizon encompassed the cluster and that in order to reduce backreaction, interaction energies within clustered masses needed to be included. Our next two extensions involved adding in extra elds, either electric charge or the cosmological constant. Finally we considered the lattices in an alternative scalar-tensor gravitational theory, Brans-Dicke. We found our lattices reduced to their relativistic versions in the appropriate limit, but for some values very far from general relativity, we could reduce backreaction to zero by altering the amount of background scalar eld. For all of our analyses we found that increasing the number of masses reduces the discrepancy between our lattice cosmologies and continuous counterparts.
AuthorsDurk, J; Queen Mary University of London
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