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

In this work, we investigate Big Bang Nucleosynthesis (BBN) within the framework of $f(T,{L}_m)$ gravity, where the gravitational Lagrangian is generalized as a function of the torsion scalar $T$ and the matter Lagrangian ${L}_m$. We analyze three representative $f(T,{L}_m)$ models and derive constraints on their free parameters, $α$ and $β$, by combining observational bounds from the freeze-out temperature with the primordial abundances of deuterium, helium-4, and lithium-7. For each model, the parameter space consistent with all elemental $Z$-constraints and the freeze-out condition is determined. These results demonstrate that $f(T,{L}_m)$ modifications can accommodate the tight observational constraints of BBN, suggesting that minimal extensions to the matter sector provide viable alternatives to the standard cosmological description and offer a promising framework for exploring modified gravity in the early Universe.