We confront $f(T,T_G)$ 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 $\Lambda$CDM paradigm. Then, we impose five specific $f(T,T_G)$ models and extract the constraints on the model parameters in order for the ratio $|\Delta T_f/T_f|$ 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, asin the power-law model, where the exponent n needs to be $n\lesssim 0.5$. 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.

中文翻译：

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f(T,TG) 引力上的大爆炸核合成约束

我们面对$F(吨,{吨}_G)$重力，具有大爆炸核合成（BBN）的要求。前者是使用拉格朗日中的扭转标量以及高斯-博内项的远平行等效项获得的，从而得到修正的弗里德曼方程，其中额外的扭转项构成有效的暗能量扇区。我们计算冻结温度的偏差${吨}_F$, 由额外的扭转项引起$\Lambda$CDM 范式。然后，我们强加了五个具体的$F(吨,{吨}_G)$模型并提取模型参数的约束，以便得到比率$|\Delta {吨}_F/{吨}_F|$以满足观测 BBN 界限。正如我们发现的那样，在大多数模型中，所涉及的参数如预期的那样被限制在其广义相对论值周围的狭窄窗口中，就像幂律模型一样，其中指数n需要为$n\lesssim 0.5$. 尽管如此，对数模型可以很容易地满足模型参数大区域的 BBN 约束。在未来的模型构建中应该考虑到这个特性。