Constraining Big Bang nucleosynthesis in f(T,B,TG,BG) gravity

Big Bang nucleosynthes describes a significant process in the early universe, responsible for the formation of light nuclei a while after the Big Bang explosion. Its sensitivity to the expansion rate makes BBN an effective probe for testing deviations from standard cosmology, particularly within the framework of modified theories of gravity. In this article, we investigate the evolution of the Universe through Big Bang nucleosynthesis within the framework of $f(T,B,T_G,B_G)$ gravity. Here, $T,B,T_G$ and $B_G$ correspond to the torsion, boundary term, teleparallel Gauss-Bonnet term, and Gauss-Bonnet boundary term, respectively. To explore the deviation from the teleparallel equivalent of general relativity, we apply the transformation $f(T,B,T_G,B_G)$ = $-T+F(T,B,T_G,B_G)$. For an in-depth analysis of the Big Bang nucleosynthesis, we choose five distinct models from gravity and compared the results with the observational limits on $\left|\frac{\Delta T_f}{T_f}\right|$ to examine restrictions on the free parameters associated with these models. Our outcomes indicate that $f(T,B,T_G,B_G)$ gravity can agree with the constraint of big bang nucleosynthesis, and hence build a valid view of the universe. Moreover, we take the limiting cases of the assumed theory, that is, $f(T,B)$ and $f\left(T\right)$ theories, which also ensure consistency with BBN data.