We reconstruct F (G) gravity theory with an exponential scale factor to realize the bouncing behavior in the early universe and examine the asymptotic behaviour of late-time solutions in this model. We propose an approach to the construction of asymptotic expansions of solutions of the Friedmann equations on the basis of Puiseux series. *

We found out that [Formula: see text] gravity theory can be rewritten in the holographic language at the level of background equivalence. The examples of the bouncing cosmological models in [Formula: see text] gravity are considered in details.