Constraining models of in?ation with a non-trivial ?eld-space by using numerical calculations of their non-Gaussianities

An era of cosmological in?ation is the preferred mechanism for producing primordial ?uctuations that are later ampli?ed to become the observed large-scale structure. Unfortunately, constraining in?ation is problematic because there are numerous models that reproduce the Gaussian power-spectrum found in the CMB. This problem is further elevated when multi?eld models are considered because the kinetic part of their Lagrangian often contains a non-trivial ?eld metric describing a curved geometry in the ?eld-space. Additionally, these models can produce measurable primordial non-Gaussianities which are now constrained in the Planck data. The non-Gaussianities of an in?ation model are measured using the bispectrum B and its amplitude fNL for a speci?c triangular template and the Gaussian statistics are described using the tensor-to-scalar ratio r and the scalar spectral index ns. In the ?rst part of this thesis, we extend the transport method, ?rst introduced by Mulryne, Seery and Wesley, to be able to calculate the power spectrum and the bispectrum and their associated observables from an in?ation model with a non-canonical ?eld metric. We implement these in a publicly available code called CppTransport to automate the calculation of the statistical properties of the primordial ?uctuations. The results of this code are tested using a model that can be described in both canonical and non-canonical ?eld coordinates with excellent agreement. We also demonstrate the code’s accuracy by comparing our bispectrum results with a separate numerical implementation of the transport method called PyTransport 2.0, again ?nding good agreement. Lastly, we consider a class of gelaton models that were predicted to produce boosted equilateral con?gurations of the bispectrum and showed this is di?cult to accomplish for models with simple potentials and a hyperbolic ?eld-space. In the second part of the thesis, we introduce a new code CpptSample, which is a CosmoSIS module that adds sampling functionality and Bayesian model selection to CppTransport. In this, we build an interface which allows the Monte-Carlo-Markov-Chain (MCMC) samplers in CosmoSIS to provide cosmological and Lagrangian initial conditions to CppTransport. The results for the primordial spectra are then passed on to the Boltzmann code CLASS to calculate the theoretical CMB power spectrum based on the underlying model and Bayesian evidence is found from the Planck2015 likelihood code. Our implementation of this retains all the extensions needed for models with a non-trivial ?eld-space and does not rely on the slow-roll approximation. We demonstrate this by calculating marginalised statistics for the quadratic, quartic, Gelaton/QSFI and a-attractor models of in?ation.