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.