Large scale vector modes and the first CMB temperature multipoles
  Recent observations have pointed out various anomalies in some multipoles (small $\ell $) of the cosmic microwave background (CMB). In this paper, it is proved that some of these anomalies could be explained in the framework of a modified concordance model, in which, there is an appropriate distribution of vector perturbations with very large spatial scales. Vector modes are associated with divergenceless (vortical) velocity fields. Here, the generation of these modes is not studied in detail (it can be done "a posteriori"); on the contrary, we directly look for the distributions of these vector modes which lead to both alignments of the second and third multipoles and a planar octopole. A general three-dimensional (3D) superimposition of vector perturbations does not produce any alignment, but we have found rather general 2D superimpositions leading to anomalies similar to the observed ones; in these 2D cases, the angular velocity has the same direction at any point of an extended region and, moreover, this velocity has the same distribution in all the planes orthogonal to it. Differential rotations can be seen as particular cases, in which, the angular velocity only depends on the distance to a rotation axis. Our results strongly suggest that appropriate mixtures of scalar and vector modes with very large spatial scales could explain the observed CMB anomalies. 
J. A. Morales and D. S\'aez