Superbounce and Loop Quantum Cosmology Ekpyrosis from Modified Gravity
  As is known, in modified cosmological theories of gravity many of the
cosmologies which could not be generated by standard Einstein gravity, can be
consistently described by $F(R)$ theories. Using known reconstruction
techniques, we investigate which $F(R)$ theories can lead to a Hubble parameter
describing two types of cosmological bounces, the superbounce model, related to
supergravity and non-supersymmetric models of contracting ekpyrosis and also
the Loop Quantum Cosmology modified ekpyrotic model. Since our method is an
approximate method, we investigate the problem at large and small curvatures.
As we evince, both models yield power law reconstructed $F(R)$ gravities, with
the most interesting new feature being that both lead to accelerating
cosmologies, in the large curvature approximation. The mathematical properties
of the some Friedmann-Robertson-Walker spacetimes $M$, that describe
superbounce-like cosmologies are also pointed out, with regards to the group of
curvature collineations $CC(M)$.
