Cosmological bouncing solutions in extended teleparallel gravity theories

In the context of extended teleparallel gravity theories with a 3 + 1-dimensional Gauss-Bonnet analog term, we address the possibility of these theories reproducing several well-known cosmological bouncing scenarios in a four-dimensional Friedmann-Lemaitre-Robertson-Walker geometry. We study which types of gravitational Lagrangians are capable of reconstructing bouncing solutions provided by analytical expressions for symmetric, oscillatory, superbounce, matter bounce, and singular bounce. Some of the Lagrangians discovered are analytical at the origin, having both Minkowski and Schwarzschild vacuum solutions. All these results open up the possibility for such theories to be competitive candidates of extended theories of gravity in cosmological scales.