Detecting a Lorentz-violating field in cosmology

We consider cosmology in the Einstein-Æther theory (the generally covariant theory of gravitation coupled to a dynamical timelike Lorentz-violating vector field) with a linear Æ-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 Æ field, both in the background cosmology and at the linear perturbation level. The primordial power spectrum of scalar perturbations in this model is shown to be the same as 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 Æ 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.