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 .