Inflationary model constraints using higher-order statistics of the primordial curvature perturbation
Anderson, Gemma Jayne
arxiv: General Relativity and Quantum Cosmology | Astrophysics::Cosmology and Extragalactic Astrophysics
Cosmological inflation is the leading candidate for the origin of structure in the Universe. However, a huge number of inflationary models currently exist. Higher-order statistics, particularly the bispectrum and trispectrum, of the primordial curvature perturbation can potentially be used to discriminate between competing models. This can provide an insight into the precise physical mechanism of inflation.\ud \ud Current constraints on inflationary models using the amplitude fNL of the bispectrum are quoted for specific templates. This results in much of the inflationary parameter space remaining unexplored. By utilizing the symmetries of the underlying quasi-de Sitter spacetime to construct a generic ‘effective field theory’ Lagrangian with adjustable parameters, one can encompass many single-field models of inflation in a unifying framework. In the first part of this thesis we perform a partial-wave decomposition of the bispectrum produced at horizon-exit by each operator in the effective Lagrangian, which we use to find the principal components using a Fisher-matrix approach. This allows us to probe much more of the parameter space. Cosmic Microwave Background bispectrum data is used to estimate the amplitude of each component, which can then translated into constraints on particular classes of single-field models. We consider the implications for DBI and ghost inflation as examples.\ud \ud In the second part of this thesis we extend the transport formalism, first introduced by Mulryne, Seery and Wesley, to calculate the trispectrum generated during superhorizon evolution in inflationary models with multiple fields. We provide transport equations that track the evolution of the local trispectrum non-linearity parameters tNL and gNL throughout inflation. We compute these for several models as examples.