  The effective action for gravity at high curvatures is likely to contain
higher derivative terms. These corrections may have profound consequences for
the singularity structure of space-time and for early Universe cosmology. In
this contribution, recent work is reviewed which demonstrates that it is
possible to construct a class of effective gravitational actions for which all
solutions with sufficient symmetries have limited curvature and are
nonsingular. Near the limiting curvature, the coupling between matter and
gravity goes to zero and in this sense the theory is asymptotically free.
