Signatures of Initial State Modifications on Bispectrum Statistics
  Modifications of the initial-state of the inflaton field can induce a
departure from Gaussianity and leave a testable imprint on the higher order
correlations of the CMB and large scale structures in the Universe. We focus on
the bispectrum statistics of the primordial curvature perturbation and its
projection on the CMB. For a canonical single-field action the three-point
correlator enhancement is localized, maximizing in the collinear limit,
corresponding to enfolded or squashed triangles in comoving momentum space. We
show that the available local and equilateral template are very insensitive to
this localized enhancement and do not generate noteworthy constraints on
initial-state modifications. On the other hand, when considering the addition
of a dimension 8 higher order derivative term, we find a dominant rapidly
oscillating contribution, which had previously been overlooked and whose
significantly enhanced amplitude is independent of the triangle under
consideration. Nevertheless, the oscillatory nature of (the sign of) the
correlation function implies the signal is nearly orthogonal to currently
available observational templates, strongly reducing the sensitivity to the
enhancement. Constraints on departures from the standard Bunch-Davies vacuum
state can be derived, but also depend on the next-to-leading terms. We
emphasize that the construction and application of especially adapted templates
could lead to CMB bispectrum constraints on modified initial states already
competing with those derived from the power spectrum.
