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[References: p. 354-355 (30 tit.)]

We explore bounce cosmology in F(G) gravity with the Gauss–Bonnet invariant G. We reconstruct F(G) gravity theory to realize the bouncing behavior in the early universe and examine the stability conditions for its cosmological solutions. It is demonstrated that the bouncing behavior with an exponential as well as a power-law scale factor naturally occurs in modified Gauss–Bonnet gravity. We also derive the F(G) gravity model to produce the ekpyrotic scenario. Furthermore, we construct the bounce with the scale factor composed of a sum of two exponential functions and show that not only the early-time bounce but also the late-time cosmic acceleration can occur in the corresponding modified Gauss–Bonnet gravity. Also, the bounce and late-time solutions in this unified model are explicitly analyzed.