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

Abstract

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.

Bayesian analysis of inflationary features in Planck and SDSS data

“…Originally, step-like inflationary potentials were postulated to study the "glitch" appearing at the low-region of the CMB anisotropy spectrum. The signatures of this class of models in the CMB temperature power spectrum and bispectrum [17][18][19][20][21][25][26][27][28][29][30][31] and in the tensor spectrum [32,33] have been studied in detail using the current data and have shown a consistent improvement of the ∆χ 2 values with respect to the featureless ΛCDM model.…”

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

“…We will show later that the effects of local features improve the agreement with CMB data but not enough to get a χ 2 as low as the one of other inflationary models with lower values of r . This type of modification of the slow-roll potential is called a local feature (LF) [39] which differs from the branch feature (BF) [39,56], since the potential is symmetric with respect to the location of the feature and it is only affected in a limited range of the scalar field value. Due to this the spectrum and bispectrum are only modified in a narrow range of scales, in contrast to the BF in which there are differences in the power spectrum between large and small scale which are absent in the case of LF.…”

“…In some cases the step in the spectrum due to a BF can be very small, and the difference between large and small scale effects would not make BF observationally distinguishable from LF. Nevertheless in general the oscillation patterns produce in the spectrum by a single BF would be different because a single LF can be considered as the combination of two appropriate BF [39].…”

“…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].…”

Scale invariance of the primordial tensor power spectrum

“…These time variations break -in a controlled way -the standard behavior required in single field slow-roll inflation, producing localized features in the spectra, though without invalidating inflation as a mechanism to explain the origin of primordial fluctuations in a way compatible with observations. Given that the source of features may be traced back to background parameters that affect the evolution of all perturbations, features appearing in different n-point correlation functions would be necessarily correlated [41][42][43][44][45][46][47][48][49][50][51][52]. In the case of scalar perturbations, a powerful way to study such time-dependent departures from slow-roll is the joint estimator analysis of two-and three-point correlation functions [52], since a detection of correlated signals in the power spectrum and bispectrum would increase the statistical significance of these features.…”