Perturbations from Inflation from Model-independent Coset Construction
Summary
A model independent theory of curvature perturbations from inflation allows a fundamental understanding of the origins of structure formation and the Cosmic Microwave Background. In this thesis we focus on the necessities to achieve this systematic and model independent way to derive a theory of curvature perturbations. We derive such a theory by applying techniques from spontaneous symmetry breaking in field theory. We approach spontaneous symmetry breaking systematically with the coset construction. We present the necessary techniques and knowledge to apply the coset construction. Any theory that is time-dependent, inflation for example, spontaneously breaks time translations. With the coset construction we describe any theory with a spontaneous symmetry breaking of time translations, i.e. all cosmology described by a single degree of freedom. In particular the coset construction leads to a theory of curvature perturbations from the early universe. We propose the steps for deriving this in non-dynamical as well as dynamical gravity. As of yet the results do not comply with the heuristic theory. The bulk of this thesis provides background on the topics, providing an overview of the concepts that enable a researcher to derive a theory of spontaneously broken time translations in dynamical and non-dynamical gravity consistent with a heuristic theory.