Big bang nucleosynthesis constraints on $$f(T,L_m)$$ gravity

Abstract We investigate Big Bang Nucleosynthesis (BBN) in the framework of $$f(T,L_m)$$ f ( T , L m ) gravity, where the gravitational Lagrangian depends on the torsion scalar T and the matter Lagrangian $$L_m$$ L m . Working within a semi-analytical BBN strategy, we encode departures from GR through the expansion-rate ratio $$Z\equiv H/H_{\textrm{GR}}$$ Z ≡ H / H GR evaluated at a characteristic freeze-out temperature and combine this with the freeze-out condition and the observationally inferred abundances of deuterium and helium-4 to constrain the free parameters of three representative EFT-motivated $$f(T,L_m)$$ f ( T , L m ) models. A distinctive aspect of $$f(T,L_m)$$ f ( T , L m ) cosmology is that the explicit $$L_m$$ L m dependence can induce an effective energy exchange between the standard component and the modified-gravity sector; we therefore derive the corresponding interaction term Q and restrict our analysis to the adiabatic regime $$\varepsilon \equiv |Q_{\textrm{rad}}/(4H\rho )|\ll 1$$ ε ≡ | Q rad / ( 4 H ρ ) | ≪ 1 throughout the BBN window, ensuring internal consistency of the temperature-based BBN mapping. Finally, to connect the radiation-era constraints with the late-time background, we present a two-fluid (dust+radiation) analysis showing how the $$L_m$$ L m -dependent corrections decouple as $$\ell \propto (1+z)^4\rightarrow 0$$ ℓ ∝ ( 1 + z ) 4 → 0 , yielding torsion-only ( f ( T ) or TEGR) cosmologies at late times on the GR-connected branch. Our results provide transparent first-pass BBN bounds on torsion–matter EFT corrections and identify viable parameter regions consistent with early-Universe data providing a controlled starting point for further early-Universe phenomenology in $$f(T,L_m)$$ f ( T , <mm