Non-Gaussianity constrains hybrid inflation

26pp, 2 figs v2: note added (see abstract)In hybrid inflationary models, inflation ends by a sudden instability associated with a steep ridge in the potential. Here we argue that this feature can generate a large contribution to the curvature perturbation on observable scales. This contribution is almost scale-invariant but highly non-Gaussian. The degree of non-Gaussianity can exceed current observational bounds, unless the inflationary scale is extremely low or the hybrid potential contains very large coupling constants. Non-linear effects on small scales may quench the non-Gaussian signal, and while we find no compelling evidence that this occurs, full lattice simulations are required to definitively address this issue. Note added: We now believe that nonlinear effects will invalidate the original computation in this paper essentially instantaneously after the short-wavelength modes reach the minimum of their potential. This means that the mechanism described in this paper will not lead to appreciatable curvature perturbations on long wavelengths, and no useful constraints on hybrid inflation will result. We have inserted a brief calculation on p2 of this manuscript to explain this fact, but have otherwise left the manuscript unchanged

Non-Gaussianity after many-field reheating

International audienceWe numerically investigate reheating after quadratic inflation with up to 65 fields, focusing on the production of non-Gaussianity. We consider several sets of initial conditions, masses, and decay rates. As expected, we find that the reheating phase can have a significant effect on the non-Gaussian signal, but that for this number of fields a detectable level of non-Gaussianity requires the initial conditions, mass range, and decay rates to be ordered in a particular way. We speculate on whether this might change in the N-flation limit

Attractor behaviour in multifield inflation

We study multifield inflation in scenarios where the fields are coupled non-minimally to gravity via $\xi_I(\phi^I)^n g^{\mu\nu}R_{\mu\nu}$, where $\xi_I$ are coupling constants, $\phi^I$ the fields driving inflation, $g_{\mu\nu}$ the space-time metric, $R_{\mu\nu}$ the Ricci tensor, and $n>0$. We consider the so-called $\alpha$-attractor models in two formulations of gravity: in the usual metric case where $R_{\mu\nu}=R_{\mu\nu}(g_{\mu\nu})$, and in the Palatini formulation where $R_{\mu\nu}$ is an independent variable. As the main result, we show that, regardless of the underlying theory of gravity, the field-space curvature in the Einstein frame has no influence on the inflationary dynamics at the limit of large $\xi_I$, and one effectively retains the single-field case. However, the gravity formulation does play an important role: in the metric case the result means that multifield models approach the single-field $\alpha$-attractor limit, whereas in the Palatini case the attractor behaviour is lost also in the case of multifield inflation. We discuss what this means for distinguishing between different models of inflation.Comment: 20 pages, 6 figures. Typos corrected and references added. This is an author-created, un-copyedited version of an article published in JCAP. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://iopscience.iop.org/article/10.1088/1475-7516/2018/06/032/pd

Transport equations for the inflationary trispectrum

We use transport techniques to calculate the trispectrum produced in multiple-field inflationary models with canonical kinetic terms. Our method allows the time evolution of the local trispectrum parameters, tauNL and gNL, to be tracked throughout the inflationary phase. We illustrate our approach using examples. We give a simplified method to calculate the superhorizon part of the relation between field fluctuations on spatially flat hypersurfaces and the curvature perturbation on uniform density slices, and obtain its third-order part for the first time. We clarify how the 'backwards' formalism of Yokoyama et al. relates to our analysis and other recent work. We supply explicit formulae which enable each inflationary observable to be computed in any canonical model of interest, using a suitable first-order ODE solver.Comment: 24 pages, plus references and appendix. v2: matches version published in JCAP; typo fixed in Eq. (54

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

Non-linear non-local Cosmology

Non-local equations of motion contain an infinite number of derivatives and commonly appear in a number of string theory models. We review how these equations can be rewritten in the form of a diffusion-like equation with non-linear boundary conditions. Moreover, we show that this equation can be solved as an initial value problem once a set of non-trivial initial conditions that satisfy the boundary conditions is found. We find these initial conditions by looking at the linear approximation to the boundary conditions. We then numerically solve the diffusion-like equation, and hence the non-local equations, as an initial value problem for the full non-linear potential and subsequently identify the cases when inflation is attained.Comment: 6 pages, 7 figures. Prepared for 4th International Workshop on The Dark Side of the Universe, BUE, 1-5 June 200

Moment transport equations for the primordial curvature perturbation

In a recent publication, we proposed that inflationary perturbation theory can be reformulated in terms of a probability transport equation, whose moments determine the correlation properties of the primordial curvature perturbation. In this paper we generalize this formulation to an arbitrary number of fields. We deduce ordinary differential equations for the evolution of the moments of zeta on superhorizon scales, which can be used to obtain an evolution equation for the dimensionless bispectrum, fNL. Our equations are covariant in field space and allow identification of the source terms responsible for evolution of fNL. In a model with M scalar fields, the number of numerical integrations required to obtain solutions of these equations scales like O(M^3). The performance of the moment transport algorithm means that numerical calculations with M >> 1 fields are straightforward. We illustrate this performance with a numerical calculation of fNL in Nflation models containing M ~ 10^2 fields, finding agreement with existing analytic calculations. We comment briefly on extensions of the method beyond the slow-roll approximation, or to calculate higher order parameters such as gNL.Comment: 23 pages, plus appendices and references; 4 figures. v2: incorrect statements regarding numerical delta N removed from Sec. 4.3. Minor modifications elsewher