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