  We study Lorentz-violating models of massive gravity which preserve rotations
and are invariant under time-dependent shifts of the spatial coordinates. In
the linear approximation the Newtonian potential in these models has an extra
``confining'' term proportional to the distance from the source. We argue that
during cosmological expansion the Universe may be driven to an attractor point
with larger symmetry which includes particular simultaneous dilatations of time
and space coordinates. The confining term in the potential vanishes as one
approaches the attractor. In the vicinity of the attractor the extra
contribution is present in the Friedmann equation which, in a certain range of
parameters, gives rise to the cosmic acceleration.
