Abstract
We study the effects of a class of features of the inflaton potential, corresponding to discontinuities in its derivatives. We perform fully numerical calculations and derive analytical approximations for the curvature perturbations spectrum and the bispectrum which are in good agreement with the numerical results. The spectrum of primordial perturbations has oscillations around the scale $$k_0$$ which leaves the horizon at the time $$\tau _0$$ when the feature occurs, with the amplitude and phase of the oscillations determined by the size and the order of the discontinuity. The large scale bispectrum in the squeezed and equilateral limits have a very similar form and are linearly suppressed. Both in the squeezed and the equilateral small scale limit the bispectrum has an oscillatory behavior whose phase depends on the parameters determining the discontinuity, and whose amplitude is inversely proportional to the scale. Given the generality of this class of features they could be used to model or classify phenomenologically different types of non-Gaussian features encountered in observational data such as the cosmic microwave background radiation or large scale structure.
Highlights
Inflation theory [10] explains the anisotropies of the cosmic microwave background (CMB) temperature as the consequence of primordial curvature perturbations whose statistical properties can be described by the n-points correlation functions
We found that each different type of feature has distinctive effects on the spectrum and bispectrum of the curvature perturbations which depend both on the order n and on the amplitude λ of the discontinuity
Curvature perturbations shows oscillations around the scale k0, which leaves the horizon at the time τ0 when the feature occurs, with amplitude and phase determined by the parameters n and λ
Summary
Inflation theory [10] explains the anisotropies of the CMB temperature as the consequence of primordial curvature perturbations whose statistical properties can be described by the n-points correlation functions. If the perturbations followed a perfectly Gaussian distribution the two points correlation function would be enough, but even the most recent observations are compatible with some non-Gaussianity corresponding to fNloLcal = 2.5 ± 5.7 and fNeqLuil = −16 ± 70 [8,11], motivating the theoretical study of the conditions which could have generated it. In this paper we focus on the effects of features of the inflaton potential on the primordial curvature perturbations, considering a class corresponding to a discontinuity in the derivatives of the potential. Our model is a generalization of other features which have been studied earlier such as the Starobinsky model or the mass step [23] These kinds of features could have arisen through different mechanisms such as for example particle production [24], or phase transitions [25], but in this paper we study their effects from a purely phenomenological point of view, without investigating their fundamental origin. The paper is organized as follows: first we define the features, we give both a numerical and analytical solution for the background, and we provide both numerical and analytical calculations of the spectrum and the bispectrum, giving details of the squeeze and equilateral limit and showing the effects of varying the different parameters defining the feature, i.e., its amplitude and the order n of the discontinuous derivatives
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