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We investigate the realization of two bouncing paradigms, namely of thesuperbounce and the loop quantum cosmological ekpyrosis, in the framework ofvarious modified gravities. In particular, we focus on the $F(R)$, $F(G)$ and$F(T)$ gravities, and we reconstruct their specific subclasses which lead tosuch universe evolutions. These subclasses constitute from power laws,polynomials, or hypergeometric ansatzes, which can be approximated by powerlaws. The qualitative similarity of different effective gravities which realizethe above two bouncing cosmologies, indicates to some universality lying behindsuch a bounce. Finally, performing a linear perturbation analysis, we show thatthe obtained solutions are conditionally or fully stable.

Superbounce and Loop Quantum Ekpyrotic Cosmologies from Modified Gravity: $F(R)$, $F(G)$ and $F(T)$ Theories