The scalar bi-spectrum in the Starobinsky model: The equilateral case

TL;DR

This paper analytically computes the scalar bi-spectrum in the Starobinsky inflation model, revealing how the non-Gaussianity parameter $nl$ depends on model parameters and can match observational values.

Contribution

It provides an exact analytical evaluation of the scalar bi-spectrum and $nl$ in the Starobinsky model, linking non-Gaussianity to the potential's slope change.

Findings

Analytical expressions for the bi-spectrum in the Starobinsky model.

$nl$ can reach values consistent with recent CMB observations.

The bi-spectrum contributions are fully analytically tractable.

Abstract

(Shortened abstract) While a featureless, nearly scale invariant, primordial scalar power spectrum fits the most recent CMB data rather well, certain features in the spectrum are known to lead to a better fit to the data (although, the statistical significance of such results remains an open issue). In the inflationary scenario, one or more periods of deviations from slow roll are necessary in order to generate features in the scalar perturbation spectrum. Over the last couple of years, it has been recognized that such deviations from slow roll inflation can also result in reasonably large non-Gaussianities. The Starobinsky model involves the canonical scalar field and consists of a linear inflaton potential with a sudden change in the slope. The change in the slope causes a brief period of departure from slow roll which, in turn, results in a sharp rise in power, along with a burst of oscillations in the scalar spectrum for modes that leave the Hubble radius just before and during the period of fast roll. The hallmark of the Starobinsky model is that it allows the scalar power spectrum to be evaluated analytically in terms of the three parameters that describe the model. We evaluate the bi-spectrum of the scalar perturbations in the Starobinsky model in the equilateral limit. Remarkably, we find that, all the different contributions to the the bi-spectrum too can be evaluated completely analytically. We show that the quantity $\fnl$, which characterizes the extent of non-Gaussianity, can be expressed purely in terms of the ratio of the two slopes on either side of the discontinuity in the potential. Further, we find that, for certain values of the parameters, $\fnl$ in the Starobinsky model can be as large as the mean value that has been arrived at from the analysis of the recent CMB data.