Suppression of scalar power on large scales and associated bispectra
  [Abridged] A sharp cut-off in the primordial scalar power spectrum on large
scales has been known to improve the fit to the cosmic microwave background
(CMB) data when compared to the more standard, nearly scale invariant power
spectrum that arises in slow roll inflation. In an earlier work, we had
numerically investigated the characteristics of the scalar bispectrum generated
in models with kinetically dominated initial conditions. In this work, we
compare the scenario with two other competing scenarios (viz. punctuated
inflation and a model due to Starobinsky) which also suppress the scalar power
in a roughly similar fashion on large scales. We further consider two other
scenarios involving inflation of a finite duration, one wherein the scalar
field begins on the inflationary attractor and another wherein the field starts
with a smaller velocity and evolves towards the attractor. These scenarios too
exhibit a sharp drop in power on large scales if the initial conditions on the
perturbations for a range of modes are imposed on super-Hubble scales as in the
kinetically dominated model. We compare the performance of all the models
against the Planck CMB data at the level of scalar power spectra. We also
compare the amplitudes and shapes of the scalar non-Gaussianity parameter
$f_{_{\rm NL}}$ in all these cases which lead to scalar power spectra of
similar form. Interestingly, we find that, in the models wherein the initial
conditions on the perturbations are imposed on super-Hubble scales, the
consistency relation governing the scalar bispectrum is violated for the large
scale modes, whereas the relation is satisfied for all the modes in the other
scenarios. These differences in the behavior of the scalar bispectra can
conceivably help us observationally discriminate between the various models
which lead to scalar power spectra of roughly similar shape.
