  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.
