  We present the solution space of the field equations in the Einstein-\ae ther
theory for the case of a $FLRW$ and a 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
