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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 $ε\simeq 0.01$ 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.