  In the context of colliding brane worlds I discuss a toy cosmological model,
developed in collaboration with E. Gravanis, which arguably produces inflation
and a relaxing to zero cosmological ``constant'' hierarchically small as
compared to the supersymmetry breaking (TeV) scale. Supersymmetry breaking is
induced by compactification of the brane worlds on magnetized tori. The crucial
ingredient is the non-criticality (non conformality) of string theory on the
observable brane world induced at the collision, which is thus viewed as a
cause for departure from equilibrium in this system. The hierarchical smallness
of the present-era vacuum energy, as compared to the SUSY breaking scale, is
thus attributed to relaxation.
