Big Bang Nucleosynthesis constraints on $f(T,T_G)$ gravity

Abstract

We confront f (T, TG) gravity, with Big Bang Nucleosynthesis (BBN) requirements. The former is obtained using both the torsion scalar, as well as the teleparallel equivalent of the Gauss-Bonnet term, in the Lagrangian, resulting to modified Friedmann equations in which the extra torsional terms constitute an effective dark energy sector. We calculate the deviations of the freeze-out temperature T f , caused by the extra torsion terms in comparison to ΛCDM paradigm. Then we impose five specific f (T, TG) models and we extract the constraints on the model parameters in order for the ratio |∆T f /T f | to satisfy the observational BBN bound. As we find, in most of the models the involved parameters are bounded in a narrow window around their General Relativity values as expected, as in the power-law model where the exponent n needs to be n 0.5. Nevertheless the logarithmic model can easily satisfy the BBN constraints for large regions of the model parameters. This feature should be taken into account in future model building.