Effects of discontinuities of the derivatives of the inflaton potential

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 τ 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.

Effects of local features of the inflaton potential on the spectrum and bispectrum of primordial perturbations

“…This is different from branch-type features which effectively divide the potential into separate branches, because they involve a step-like function in their definition. Some examples of branch-type features are the Starobinsky model [27] and its generalizations [33,35]. In BF models the spectrum can, for example, exhibit a step, Table 1 Fig.…”

“…The type of feature we study in this paper differs from [33] in the fact that here we study only local features, which only affect the potential in a limited range of the field values, while in [33] the features are not local and modify the potential for an entire branch, due to the absence of any dumping factor (Fig. 3).…”

“…It is important to observe that both the spectrum and the bispectrum are only affected in a limited range of scales, since this is a LF. For a BF, instead, the change affects all the scales before of after the feature [33,45], because the potential is modified in the entire branch.…”

“…The Starobinsky model and its generalizations [32][33][34][35][36] belong to a class of branch features (BFs) which involve a step function or a smoothed version of the latter [37], and consequently introduce a distinction between a left and right branch of the potential. In this paper instead we will consider the effects of local features (LF) [38] which only modify the potential locally in field space, while leaving it unaffected sufficiently far from the feature.…”

CMB anomalies and the effects of local features of the inflaton potential

“…Features of the inflaton potential can affect the evolution of primordial curvature perturbations [1, and consequently generate a variation in the amplitude of the spectrum and bispectrum [38][39][40][41][42][43][44][45][46]56]. This can provide a better fit of the observational data in the regions where the spectrum shows some deviations from a power law [1][2][3]40,41,[43][44][45][46]51,52,[60][61][62].…”