Observable predictions of generalised inflationary scenarios

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.Comment: PhD Thesis, Queen Mary, University of London. Supervised by Reza Tavakol. (212 pages, 31 figures

General analytic predictions of two-field inflation and perturbative reheating

16 pages, 5 figures, Version 2 includes a revised comparison with Meyers and Tarrant [41

The curvature perturbation at second order

We give an explicit relation, up to second-order terms, between scalar-field fluctuations defined on spatially-flat slices and the curvature perturbation on uniform-density slices. This expression is a necessary ingredient for calculating observable quantities at second-order and beyond in multiple-field inflation. We show that traditional cosmological perturbation theory and the `separate universe' approach yield equivalent expressions for superhorizon wavenumbers, and in particular that all nonlocal terms can be eliminated from the perturbation-theory expressions

The inflationary bispectrum with curved field-space

We compute the covariant three-point function near horizon-crossing for a system of slowly-rolling scalar fields during an inflationary epoch, allowing for an arbitrary field-space metric. We show explicitly how to compute its subsequent evolution using a covariantized version of the separate universe or "delta-N" expansion, which must be augmented by terms measuring curvature of the field-space manifold, and give the nonlinear gauge transformation to the comoving curvature perturbation. Nonlinearities induced by the field-space curvature terms are a new and potentially significant source of non-Gaussianity. We show how inflationary models with non-minimal coupling to the spacetime Ricci scalar can be accommodated within this framework. This yields a simple toolkit allowing the bispectrum to be computed in models with non-negligible field-space curvature.Comment: 22 pages, plus appendix and reference

Evolution of fNL to the adiabatic limit

We study inflationary perturbations in multiple-field models, for which zeta typically evolves until all isocurvature modes decay--the "adiabatic limit". We use numerical methods to explore the sensitivity of the nonlinear parameter fNL to the process by which this limit is achieved, finding an appreciable dependence on model-specific data such as the time at which slow-roll breaks down or the timescale of reheating. In models with a sum-separable potential where the isocurvature modes decay before the end of the slow-roll phase we give an analytic criterion for the asymptotic value of fNL to be large. Other examples can be constructed using a waterfall field to terminate inflation while fNL is transiently large, caused by descent from a ridge or convergence into a valley. We show that these two types of evolution are distinguished by the sign of the bispectrum, and give approximate expressions for the peak fNL.Comment: v1: 25 pages, plus Appendix and bibliography, 6 figures. v2: minor edits to match published version in JCA

Chaotic inflation in modified gravitational theories

We study chaotic inflation in the context of modified gravitational theories. Our analysis covers models based on (i) a field coupling $\omega(\phi)$ with the kinetic energy $X$ and a nonmimimal coupling $\zeta \phi^{2} R/2$ with a Ricci scalar $R$, (ii) Brans-Dicke (BD) theories, (iii) Gauss-Bonnet (GB) gravity, and (iv) gravity with a Galileon correction. Dilatonic coupling with the kinetic energy and/or negative nonminimal coupling are shown to lead to compatibility with observations of the Cosmic Microwave Background (CMB) temperature anisotropies for the self-coupling inflaton potential $V(\phi)=\lambda \phi^{4}/4$. BD theory with a quadratic inflaton potential, which covers Starobinsky's $f(R)$ model $f(R)=R+R^{2}/(6M^{2})$ with the BD parameter $\omega_{BD}=0$, gives rise to a smaller tensor-to-scalar ratio for decreasing $\omega_{BD}$. In the presence of a GB term coupled to the field $\phi$, we express the scalar/tensor spectral indices $n_{s}$ and $n_{t}$ as well as the tensor-to-scalar ratio $r$ in terms of two slow-roll parameters and place bounds on the strength of the GB coupling from the joint data analysis of WMAP 7yr combined with other observations. We also study the Galileon-like self-interaction $\Phi(\phi) X \square\phi$ with exponential coupling $\Phi(\phi) \propto e^{\mu\phi}$. Using a CMB likelihood analysis we put bounds on the strength of the Galileon coupling and show that the self coupling potential can in fact be made compatible with observations in the presence of the exponential coupling with $\mu>0$.Comment: 28 pages, 8 figure