General quadrupolar statistical anisotropy: Planck limits
  Several early Universe scenarios predict a direction-dependent spectrum of primordial curvature perturbations. This translates into the violation of the statistical isotropy of cosmic microwave background radiation. Previous searches for statistical anisotropy mainly focussed on a quadrupolar direction-dependence characterised by a single multipole vector and an overall amplitude $g_*$. Generically, however, the quadrupole has a more complicated geometry described by two multipole vectors and $g_*$. This is the subject of the present work. In particular, we limit the amplitude $g_*$ for different shapes of the quadrupole by making use of Planck 2015 maps. We also constrain certain inflationary scenarios which predict this kind of more general quadrupolar statistical anisotropy. 
S. Ramazanov, G. Rubtsov, M. Thorsrud, F. R. Urban
astro-ph.CO hep-th