  We consider cosmology in the Einstein-aether theory (the generally covariant
theory of gravitation coupled to a dynamical timelike Lorentz-violating vector
field) with a linear aether-Lagrangian. The 3+1 spacetime splitting approach is
used to derive covariant and gauge invariant perturbation equations which are
valid for a general class of Lagrangians. Restricting attention to the
parameter space of these theories which is consistent with local gravity
experiments, we show that there are tracking behaviors for the aether field,
both in the background cosmology and at linear perturbation level. The
primordial power-spectrum of scalar perturbations in this model is shown to be
the same that predicted by standard general relativity. However, the
power-spectrum of tensor perturbation is different from that in general
relativity, but has a smaller amplitude and so cannot be detected at present.
We also study the implications for late-time cosmology and find that the
evolution of photon and neutrino anisotropic stresses can source the aether
field perturbation during the radiation and matter dominated epochs, and as a
result the CMB and matter power spectra are modified. However these effects are
degenerate with respect to other cosmological parameters, such as neutrino
masses and the bias parameter in the observed galaxy spectrum.
