Theoretical and observational aspects of inflationary cosmology

Abstract

A testable theory of the universe has come up with Einstein's theory of general relativity. Combination of the theory with fundamental physics has provided significant understanding of the universe in the light of modern cosmological observations. On the other hand, the success of the hot Big Bang and Λ-CDM relies on the existence of dark energy and dark matter which are beyond the standard model of particle physics. Another required extension is inflationary mechanism which was suggested as a resolution to shortcomings Big Bang such as horizon and flatness problems. However, the biggest success of the inflationary paradigm is to explain the generation of initial perturbations that are responsible for the structure formation in the universe. A scalar field, called inflaton, leads to a exponential expansion in the early stage of the universe. Although inflation is a very strong theory for the early universe, direct test of the theory is not possible due to extremely-high energy scales. Instead, inflationary models are tested against observations come from imprints of the primordial density perturbations. An important pair of parameters that comes from the observations are spectral index n_s and tensor-to-scalar ratio r. Many inflationary models rely on slow--roll mechanism in which the inflaton slowly rolls through its potential minima so that equation of state parameter satisfies the acceleration condition ω < -1/3. Slow--roll parameters are used to dictate such behaviour to the inflaton field. Besides, perturbations and therefore inflationary observables can be expressed in terms of slow--roll parameters. Despite the fact that various minimally coupled single field models are consistent with current observations, quantum field theory in curved space anticipates a non-minimal coupling of scalar field to curvature scalar R. In this study, inflationary dynamics within the context of general relativity and scalar--tensor theories of gravitation is investigated. In the minimally coupled case, inflaton with a potential of the form φ^n is studied. In the non-minimally coupled case, same model with a coupling F(φ) = 1 + ξ φ^2 to curvature scalar is examined. In order to study inflation in scalar--tensor theories, usually conformal transformations are used, and for convenience the analysis is performed in Einstein Frame. In addition to standard Einstein frame analysis, we also perform the analysis in the Jordan frame. The predictions of the models are compared with PLANCK dataset using CosmoMC.