  We investigate the breaking of global statistical isotropy caused by a dark
energy component with an energy-momentum tensor which has point symmetry, that
could represent a cubic or hexagonal crystalline lattice. In such models
Gaussian, adiabatic initial conditions created during inflation can lead to
anisotropies in the cosmic microwave background whose spherical harmonic
coefficients are correlated, contrary to the standard assumption. We develop an
adaptation of the line of sight integration method that can be applied to
models where the background energy-momentum tensor is isotropic, but whose
linearized perturbations are anisotropic. We then show how this can be applied
to the cases of cubic and hexagonal symmetry. We compute quantities which show
that such models are indistinguishable from isotropic models even in the most
extreme parameter choices, in stark contrast to models with anisotropic initial
conditions based on inflation. The reason for this is that the dark energy
based models contribute to the CMB anistropy via the inegrated Sachs-Wolfe
effect, which is only relevent when the dark energy is dominant, that is, on
the very largest scales. For inflationary models, however, the anisotropy is
present on all scales.
