Reduced Lagrangians and analytic solutions in Einstein-aether cosmology

We present the solution space of the field equations in the Einstein-aether theory for the case of a FLRW and a locally rotationally symmetric (LRS) Bianchi type III space-time. We also find that there are portions of the initial parameters space for which no solution is admitted by the reduced equations. The reduced Lagrangians deduced from the full action are, in general, correctly describing the dynamics whenever solutions do exist. Finally in the FLRW case a curvature singularity exists, while in the type III there are choices of the range of parametres for which there is no curvature singularity.