  Near the singularity, gravity should be modified to an effective theory, in
the same sense as with the Euler-Heisenberg electrodynamics. This effective
gravity surmounts to higher derivative theory, and as is well known, a much
more reacher theory concerning the solution space. On the other hand, as a
highly non linear theory, the understanding of this solution space must go
beyond the linearized approach. In this talk we will present some results
previously published by collaborators and myself, concerning solutions for
vacuum spatially homogenous cases of Bianchi types $I$ and $VII_A$. These are
the anisotropic generalizations of the cosmological spatially "flat", and
"open" models respectively. The solutions present isotropisation in a weak
sense depending on the initial condition. Also, depending on the initial
condition, singular solutions are obtained.
