*Article* **Big Bang Nucleosynthesis Constraints on** *f* (*T***,** *TG*) **Gravity**

**Petros Asimakis 1 , Emmanuel N. Saridakis 2,3,4, \* , Spyros Basilakos 2,5,6 and Kuralay Yesmakhanova 7,8**


**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<sup>f</sup>* , caused by the extra torsion terms in comparison to ΛCDM paradigm. Then, we impose five specific *f*(*T*, *TG*) models and extract the constraints on the model parameters in order for the ratio |∆*T<sup>f</sup>* /*T<sup>f</sup>* | 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, asin 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.

**Keywords:** modified gravity; nucleosynthesis; torsional gravity

**PACS:** 98.80.−k; 04.50.Kd; 26.35.+c; 98.80.Es
