We study inflationary perturbations in multiple-field models, for which ζ typically evolves until all isocurvature modes decay-the "adiabatic limit". We use numerical methods to explore the sensitivity of the local-shape bispectrum 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 f NL to be large. Other examples can be constructed using a waterfall field to terminate inflation while f NL 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 f NL .

Abstract. 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 'δN ' 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 study chaotic inflation in the context of modified gravitational theories. Our analysis covers models based on (i) a field coupling ω(φ) with the kinetic energy X = −(1/2)g µν ∂µφ∂νφ and a nonmimimal coupling ζφ 2 R/2 with a Ricci scalar R, (ii) Brans-Dicke (BD) theories, (iii) GaussBonnet (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 (φ) = λφ 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 ωBD = 0, gives rise to a smaller tensor-toscalar ratio for decreasing ωBD. In the presence of a GB term coupled to the field φ, we express the scalar/tensor spectral indices ns and nt as well as the tensor-to-scalar ratio r in terms of two slowroll 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 Φ(φ)X φ with exponential coupling Φ(φ) ∝ e µφ . 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 µ > 0.

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. IntroductionAccording to our current ideas, structure in the universe was seeded by quantum fluctuations which were amplified during an inflationary epoch. During inflation these fluctuations dominate the variation in energy density from place to place and therefore generate a gravitational response which can be probed by cosmological observations. Inflationary amplification is believed to occur for any sufficiently light degree of freedom, in the sense that its mass m was substantially less than the Hubble rate H while scales of interest were being carried beyond the horizon. Models motivated by modern concepts in high-energy physics often invoke many light fields, and therefore can be tested only if we have an understanding of their effects. The literature surrounding calculations of the inflationary density perturbation is now very mature-often with agreement on subtle effects to second-or even third-order in perturbation theory-which allows these effects to be predicted in some detail. But despite this maturity it is remarkable that no completely explicit formula has been given for the uniform-density gauge curvature perturbation in an inflationary model with an arbitrary number of fields. 1 A formula of this type would give the next-order term in the classic result ζ = −φ α δφ α /2M 2 P Hǫ which has long been known at first order. It is a key element in computing non-Gaussian signatures in the statistics of the inflationary density perturbation. Here and below, ǫ ≡ −Ḣ/H 2 is the usual slow-roll parameter and δφ α labels the species of light fields.In this paper we supply the missing formula, valid for an arbitrary number of canonical fields and without using the slow-roll approximation. We perform the calculation using two independent methods: traditional 'cosmological perturbation theory', which is an expansion in the amplitude of small fluctuations around a Robertson-Walker background, and the 'separate universe approach', which is an expansion in the amplitude of gradients of the perturbations. In practice (although not required in principle), separate-universe calculations often invoke a second expansion in the amplitude of the fluctuations, after which the two methods should agree for any Fourier mode much larger than the cosmological horizon. For a mode of wavenumber k this requires k/aH ≪ 1, making spatial gradients negligible. We verify that the two approaches give equivalent answers and clarify some issues regarding nonlocal terms which ...

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 'heat-map' approach developed by Byrnes et al. The conditions required to generate a large trispectrum are broadly the same as those that can produce a large bispectrum. We derive a simple relation between τ NL and f NL for models with separable potentials, and furthermore show that g NL and τ NL 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 f NL , τ NL and g NL are sourced by generic shapes in the inflationary potential, namely ridges, valleys and inflection points.