Noether Symmetries in Gauss-Bonnet-teleparallel cosmology

A generalized teleparallel cosmological model, $f(T_{\mathcal{G}},T)$, containing the torsion scalar $T$ and the teleparallel counterpart of the Gauss-Bonnet topological invariant $T_{\mathcal{G}}$, is studied in the framework of the Noether Symmetry Approach. As $f(\mathcal{G},R)$ gravity, where $\mathcal{G}$ is the Gauss-Bonnet topological invariant and $R$ is the Ricci curvature scalar, exhausts all the curvature information that one can construct from the Riemann tensor, in the same way, $f(T_{\mathcal{G}},T)$ contains all the possible information directly related to the torsion tensor. In this paper, we discuss how the Noether Symmetry Approach allows to fix the form of the function $f(T_{\mathcal{G}},T)$ and to derive exact cosmological solutions.