Quantitative bispectra from multifield inflation

Abstract

After simplifying and improving the non-Gaussian formalism we developed in previous work, we derive a quantitative expression for the three-point correlator (bispectrum) of the curvature perturbation in general multiple-field inflation models. Our result describes the evolution of non-Gaussianity on superhorizon scales caused by the nonlinear influence of isocurvature perturbations on the adiabatic perturbation during inflation. We then study a simple quadratic two-field potential and find that when slow roll breaks down and the field trajectory changes direction in field space, the nonGaussianity can become large. However, for the simple models studied to date, the magnitude of this non-Gaussianity decays away after the isocurvature mode is converted into the adiabatic mode.

Classical approximation to quantum cosmological correlations

“…10) 11) where the superscript (0) denotes the free field correlation functions. They obey the identity 12) and they can be put together in a matrix:…”

“…for calculating non-Gaussianities perturbatively in multifield inflation [8,9,10,11], and for investigating nonperturbative behaviour in de Sitter space that occurs at very late times [64,65], when the factors ln(−τ ) have grown so large that they overcome the suppression by small coupling constants. In the latter case it has been argued [64,65] that the stochastic approach can reproduce the terms with the largest power of ln(−τ ) at each order in the coupling constant (leading log approximation).…”

“…those involving multiple fields, the curvature perturbation ζ is not constant after horizon exit. Therefore evolution after horizon exit might lead to non-Gaussian effects, which has been investigated in [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]. These investigations have been done by solving classical equations of motion, which is assumed to be a good approximation to the quantum theory, because quantum effects are presumably negligible for wavelengths much longer than the horizon length (see [28] for a recent argument).…”

Non-Gaussianity in two-field inflation

“…Moreover, it has not been wholly clear why it is so difficult to produce large non-Gaussianity in such models. Though some authors [31,32,41,44,45,47] have found spikes in nonGaussianity whenever the inflaton trajectory changes direction sharply, these spikes in non-Gaussianity are transient and die away before the end of inflation. That makes a comprehensive study of non-Gaussianity generation timely, to understand any circumstances under which observably large non-Gaussianity arises in such models.…”

“…However, if inflation is described by some non-minimal modification, such as multiple fields or higher derivative operators in the inflationary Lagrangian, then non-Gaussianity might be observable in the near future. Indeed, there have been many attempts to calculate the level of non-Gaussianity in general multi-field models (e.g., [31][32][33][34][35][36][37][38][39][40][41][42]), as well as in two-field models (e.g., [43][44][45][46][47][48][49][50][51]). However, it has been very difficult to find models that produce large nonGaussianity, though some exceptions have been found such as in the curvaton model [52][53][54][55][56][57][58], hybrid and multibrid inflation (e.g., [59][60][61][62][63][64][65][66][67]), in certain modulated and tachyonic (p)re-heating scenarios (e.g., [68][69][70][71][72][73][74]), and in some quadratic small-field, two-field models by taking appropriate care of loop correc...…”