| Summary: | Cosmic topology is difficult to constrain due to the lack of observable phenomena which are affected by this property of the Universe. The phenomenon with the most potential to reveal cosmic topology is the cosmic microwave background (CMB). The task of constraining topology with the CMB is challenging, and so the more data that is utilised the better. This thesis sets out a method that uses the full information available from the CMB, including polarisation, in the form of a Bayesian analysis of the full correlation matrix of the CMB. A catalogue of flat spaces is presented, of which four are analysed here; the remainder could be analysed with minimal modifications to the code developed in this work. With a little more modification, the code could also be utilised to investigate spherical and hyperbolic spaces. The four topologies analysed here are the flat torus, half turn space, Klein space and Klein space with vertical flip. More work needs to be done on the Bayesian analysis in order to achieve constraints on these four spaces; efforts in this work were concentrated on efficiently generating full correlation matrices. The code developed for this task is capable of generating at least 231 individual correlation matrices for a given topology (the parameters varied being the size and cosmology of the Universe, as well as the type of correlation, e.g. TT), for a CMB resolution of l = 30 and a spatial resolution of k = 100/L (where k are Fourier modes and L is the size of the Universe), on an entry level server in less than one day.
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