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Connecting Inflation to Observations Through the Bispectrum 10.17863/CAM.87014 Clarke, Philip Shellard, Paul Numerically calculating the full primordial bispectrum predicted by a model of inflation and comparing it to what we see in the CMB sky is very computationally intensive, necessitating layers of approximations and limiting the models which can be constrained. The inherent separability of the tree level in-in formalism provides a means by which to obviate some of these difficulties. To exploit this property, one can expand in separable basis functions. The practicality of this method is then determined by the descriptive power of the basis chosen, i.e. by the range of scenarios for which that basis provides a convergent representation of the bispectrum. The central difficulty encountered in obtaining fast convergence is the effect of dominant non-physical k-configurations. A secondary difficulty encountered is accurately including the early-time contributions to the higher-order coefficients (which are necessary to capture feature effects, such as resonance non-Gaussianity). In this thesis we develop this separable, template-free approach into a practical and efficient numerical methodology which can be applied to a much wider and more complicated range of bispectrum phenomenology than previous analyses. This is an important step forward towards observational pipelines which can fully exploit the information contained in the primordial bispectrum to directly confront specific models of inflation. We use our implementation of this pipeline to obtain a constraint on DBI inflation, and validate our implementation by comparing this constraint to an equivalent one obtained by the Planck collaboration. University of Cambridge 2022-03-01 Thesis Doctoral Doctor of Philosophy (PhD) eng https://www.repository.cam.ac.uk/handle/1810/339597 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/23769b10-9fe9-46a8-bfa8-8b5bf7fb6114/download d6dcefc71fc46faefb04253b162e915e https://www.rioxx.net/licenses/all-rights-reserved/ inflation