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

Abstract

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 we 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, as in 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.

arXiv comment9 pages, 3 figures, invited paper to appear in Universe Special Issue "Torsion-Gravity and Spinors in Fundamental Theoretical Physics", Special Issue Editor: Luca Fabbri

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• Growth factor in teleparallel Gauss-Bonnet gravity