  We investigate the quantized versions of Born Infeld electrodynamics and Born
Infeld Gravity. We derive Feynman rules for B-I electrodynamics by deriving an
effective Lagrangian with the square root removed using the Faddeev-Popov
method. In the case of B-I gravity, the square root in the Lagrangian is
removed by the introduction of the Vierbien fields. This approach has the
advantage that SO(3,1) can be consistently regarded to be the gauge group of
gravity. Finally, using a rough argument, the quantum fluctuations of the radii
of spatial hypersurfaces in flat space are shown to undergo accelerated
increase with time.
