Anisotropic non-Gaussianity from Rotational Symmetry Breaking Excited
  Initial States
  If the initial quantum state of the primordial perturbations broke rotational
invariance, that would be seen as a statistical anisotropy in the angular
correlations of the cosmic microwave background radiation (CMBR) temperature
fluctuations. This can be described by a general parameterisation of the
initial conditions that takes into account the possible direction-dependence of
both the amplitude and the phase of particle creation during inflation. The
leading effect in the CMBR two-point function is typically a quadrupole
modulation, whose coefficient is analytically constrained here to be $|B|
\lesssim 0.06$. The CMBR three-point function then acquires enhanced
non-gaussianity, especially for the local configurations. In the large
occupation number limit, a distinctive prediction is a modulation of the
non-gaussianity around a mean value depending on the angle that short and long
wavelength modes make with the preferred direction. The maximal variations with
respect to the mean value occur for the configurations which are coplanar with
the preferred direction and the amplitude of the non-gaussianity increases
(decreases) for the short wavelength modes aligned with (perpendicular to) the
preferred direction. For a high scale model of inflation with maximally pumped
up isotropic occupation and $\epsilon\simeq 0.01$ the difference between these
two configurations is about $0.27$, which could be detectable in the future.
For purely anisotropic particle creation, the non-Gaussianity can be larger and
its anisotropic feature very sharp. The non-gaussianity can then reach $f_{NL}
\sim 30$ in the preferred direction while disappearing from the correlations in
the orthogonal plane.
