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Inflation is an early period of accelerated cosmic expansion, thought to be sourced by high energy physics. A key task today is to use the influx of increasingly precise observational data to constrain the plethora of inflationary models suggested by fundamental theories of interactions. This requires a robust theoretical framework for quantifying the predictions of such models; helping to develop such a framework is the aim of this thesis. We provide the first complete quantization of subhorizon perturbations for the well-motivated class of multi-field inflationary models with a non-trivial field metric, which we show may yield interesting signatures in the bispectrum of the Cosmic Microwave Background (CMB). The subsequent evolution of perturbations in the superhorizon epoch is then considered, via a covariant extension of the transport formalism. To develop intuition about the relationship between inflationary dynamics and the evolution of cosmic observables, we investigate analytic approximations of superhorizon perturbation evolution. The validity of these analytic results is contingent on reaching a state of adiabaticity which we discuss and illustrate in depth. We then apply our analytic methods to elucidate the types of inflationary dynamics that lead to an enhanced CMB non-Gaussianity, both in its bispectrum and trispectrum. In addition to deriving a number of new simple relations between the non-Gaussianity parameters, we explain dynamically how and why different shapes of inflationary potential lead to particular observational signatures. Candidate theories of high energy physics such as low energy effective string theory also motivate single-field modifications to the Einstein-Hilbert action. We show how a range of such corrections allow for consistency of single-field chaotic inflationary models that are otherwise in tension with observational data.
We use the Hamilton--Jacobi formalism to constrain the space of possible single field, inflationary Hubble flow trajectories when compared to the WMAP and Planck satellites Cosmic Microwave Background (CMB) results. This method yields posteriors on t
We carry out a numerical calculation of the bispectrum in generalised trajectories of canonical, single--field inflation. The trajectories are generated in the Hamilton-Jacobi (HJ) formalism based on Hubble Slow Roll (HSR) parameters. The calculation
In a logamediate inflationary universe model we introduce the curvaton field in order to bring this inflationary model to an end. In this approach we determine the reheating temperature. We also outline some interesting constraints on the parameters
While the topology of the Universe is at present not specified by any known fundamental theory, it may in principle be determined through observations. In particular, a non-trivial topology will generate pairs of matching circles of temperature fluct
An important, and potentially detectable, signature of a non-trivial topology for the universe is the presence of so called circles-in-the-sky in the cosmic microwave background (CMB). Recent searches, confined to antipodal and nearly antipodal circl