  We discuss the cosmological reconstruction in modified Gauss-Bonnet and F(R)
gravities. Two alternative representations of the action (with and without
auxiliary scalar) are considered. The approximate description of
deceleration-acceleration transition cosmologies is reconstructed. It is shown
that cosmological solution containing Big Bang and Big Rip singularities may be
reconstructed only using the representation with the auxiliary field. The
analytical description of the deceleration-acceleration transition cosmology in
modified Gauss-Bonnet gravity is demonstrated to be impossible at sufficiently
general conditions.
