  We find a simple modification of the longitudinal mode in General Relativity
which incorporates the idea of limiting curvature. In this case the
singularities in contracting Friedmann and Kasner universes are avoided, and
instead, the universe has a regular bounce which takes place during the time
inversely proportional to the square root of the limiting curvature. Away from
the bounce, corrections to General Relativity are negligible. In addition the
non-singluar modification of General Relativity delivers for free a realistic
candidate for Dark Matter.
