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

Abstract

We investigate Big Bang Nucleosynthesis (BBN) in the framework of

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 , L m )

gravity.