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.

We study the effects of a class of features of the potential of slow-roll inflationary models corresponding to a step symmetrically dumped by an even power negative exponential factor, which we call local features. Local-type features differ from other branch-type features considered previously, because the potential is only affected in a limited range of the scalar field value, and they are symmetric with respect to the location of the feature. This type of feature only affects the spectrum and bispectrum in a narrow range of scales which leave the horizon during the time interval corresponding to the modification of the potential. On the contrary branch-type features have effects on all the perturbation modes leaving the horizon when the field value is within the interval defining the branch, introducing for example differences in the power spectrum between large and small scale which are absent in the case of local-type features. The spectrum and bispectrum of primordial curvature perturbations are affected by oscillations around the scale k 0 exiting the horizon at the time τ 0 corresponding to the feature. We also compute the effects of the features on the CMB temperature and polarization spectra, showing the effects of different choices of parameters.

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Recent analysis of the WMAP and Planck data have shown the presence of a dip and a bump in the spectrum of primordial perturbations at the scales k = 0.002 Mpc −1 and k = 0.0035 Mpc −1 , respectively. We analyze for the first time the effects of a local feature in the inflaton potential to explain the observed deviations from scale invariance in the primordial spectrum. We perform a best-fit analysis of the cosmic microwave background (CMB) radiation temperature and polarization data. The effects of the features can improve the agreement with observational data respect to the featureless model. The best-fit local feature affects the primordial curvature spectrum mainly in the region of the bump, leaving the spectrum unaffected on other scales.

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We study the degeneracy of the primordial spectrum and bispectrum of the curvature perturbation in single field inflationary models with a class of features in the inflaton potential. The feature we consider is a discontinuous change in the shape of the potential and is controlled by a couple of parameters that describe the strength of the discontinuity and the change in the potential shape.This feature produces oscillations of the spectrum and bispectrum around the comoving scale k = k 0 that exits the horizon when the inflaton passes the discontinuity. We find that the effects on the spectrum and almost all configurations of the bispectrum including the squeezed limit depend on a single quantity which is a function of the two parameters defining the feature. This leads to a degeneracy, i.e. different features of the inflaton potential can produce the same observational effects.However, we find that the degeneracy in the bispectrum is removed at the equilateral limit around k = k 0 . This can be used to discriminate different models which give the same spectrum.

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