  We consider anisotropic cosmologies in a particular shift-symmetric Horndeski
theory containing the $G^{\mu\nu}\partial_\mu\phi \partial_\nu\phi$ coupling,
where $G^{\mu\nu}$ is the Einstein tensor. This theory admits stable in the
future self-accelerating cosmologies whose tensor perturbations propagate with
the velocity very close to the speed of light such that the theory agrees with
the gravity wave observations. Surprisingly, we find that the anisotropies
within the Bianchi I homogeneous spacetime model are screened at early time by
the scalar charge, whereas at late times they are damped in the usual way.
Therefore, contrary to what one would normally expect, the early state of the
universe in the theory cannot be anisotropic and (locally) homogeneous in the
absence of spatial curvature. The early universe cannot be isotropic either,
because it should then be unstable with respect to inhomogeneous perturbations.
As a result, the early universe should be inhomogeneous. At the same time, we
find that in the spatially curved Bianchi IX case the anisotropies can be
strong at early times even in the presence of a scalar charge.
