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 observational signatures of multi-field inflation will generally evolve as the Universe reheats. We introduce a general analytic formalism for tracking this evolution through perturbative reheating, applicable to two field models with arbitrary s
eparable potentials. The various transitions, including the onset of scalar field oscillations and the reheating of each field, can happen in different orders and on arbitrary hypersurfaces. The effective equations of state of the oscillating fields are also arbitrary. Nevertheless, our results are surprisingly simple. Our formalism encapsulates and generalises a huge range of previous calculations including two-field inflation, spectator models, the inhomogeneous end of inflation scenario and numerous generalised curvaton 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.
Planck data has not found the smoking gun of non-Gaussianity that would have necessitated consideration of inflationary models beyond the simplest canonical single field scenarios. This raises the important question of what these results do imply for
more general models, and in particular, multi-field inflation. In this paper we revisit four ways in which two-field scenarios can behave differently from single field models; two-field slow-roll dynamics, curvaton-type behaviour, inflation ending on an inhomogeneous hypersurface and modulated reheating. We study the constraints that Planck data puts on these classes of behaviour, focusing on the latter two which have been least studied in the recent literature. We show that these latter classes are almost equivalent, and extend their previous analyses by accounting for arbitrary evolution of the isocurvature mode which, in particular, places important limits on the Gaussian curvature of the reheating hypersurface. In general, however, we find that Planck bispectrum results only constrain certain regions of parameter space, leading us to conclude that inflation sourced by more than one scalar field remains an important possibility.
We find constraints on inflationary dynamics that yield a large local bispectrum and/or trispectrum during two-field slow-roll inflation. This leads to simple relations between the non-Gaussianity parameters, simplifying the Suyama-Yamaguchi inequali
ty and also producing a new result between the trispectrum parameters tNL and gNL.
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 us
ing 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.
We calculate the conditions required to produce a large local trispectrum during two-field slow-roll inflation. This is done by extending and simplifying the heatmap approach developed by Byrnes et al. The conditions required to generate a large tris
pectrum are broadly the same as those that can produce a large bispectrum. We derive a simple relation between tauNL and fNL for models with separable potentials, and furthermore show that gNL and tauNL can be related in specific circumstances. Additionally, we interpret the heatmaps dynamically, showing how they can be used as qualitative tools to understand the evolution of non-Gaussianity during inflation. We also show how fNL, tauNL and gNL are sourced by generic shapes in the inflationary potential, namely ridges, valleys and inflection points.
We study the evolution of non-Gaussianity in multiple-field inflationary models, focusing on three fundamental questions: (a) How is the sign and peak magnitude of the non-linearity parameter fNL related to generic features in the inflationary potent
ial? (b) How sensitive is fNL to the process by which an adiabatic limit is reached, where the curvature perturbation becomes conserved? (c) For a given model, what is the appropriate tool -- analytic or numerical -- to calculate fNL at the adiabatic limit? We summarise recent results obtained by the authors and further elucidate them by considering an inflection point model.
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.
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 Starobinskys $f(R)$ 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 $Phi(phi) X squarephi$ with exponential coupling $Phi(phi) propto e^{muphi}$. 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 $mu>0$.
