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

Abstract We investigate Big Bang Nucleosynthesis (BBN) in the framework of $$f(T,L_m)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>T</mml:mi> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>m</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> gravity, where the gravitational Lagrangian depends on the torsion scalar T and the matter Lagrangian $$L_m$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>m</mml:mi> </mml:msub> </mml:math> . Working within a semi-analytical BBN strategy, we encode departures from GR through the expansion-rate ratio $$Z\equiv H/H_{\textrm{GR}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Z</mml:mi> <mml:mo>≡</mml:mo> <mml:mi>H</mml:mi> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>H</mml:mi> <mml:mtext>GR</mml:mtext> </mml:msub> </mml:mrow> </mml:math> 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 $$f(T,L_m)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>T</mml:mi> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>m</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> models. A distinctive aspect of $$f(T,L_m)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>T</mml:mi> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>m</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> cosmology is that the explicit $$L_m$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>m</mml:mi> </mml:msub> </mml:math> 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 $$\varepsilon \equiv |Q_{\textrm{rad}}/(4H\rho )|\ll 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mi>ε</mml:mi> <mml:mo>≡</mml:mo> <mml:mo>|</mml:mo> </mml:mrow> <mml:msub> <mml:mi>Q</mml:mi> <mml:mtext>rad</mml:mtext> </mml:msub> <mml:mrow> <mml:mo>/</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>4</mml:mn> <mml:mi>H</mml:mi> <mml:mi>ρ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>|</mml:mo> <mml:mo>≪</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mrow> </mml:math> 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 $$L_m$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>m</mml:mi> </mml:msub> </mml:math> -dependent corrections decouple as $$\ell \propto (1+z)^4\rightarrow 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ℓ</mml:mi> <mml:mo>∝</mml:mo> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>z</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mn>4</mml:mn> </mml:msup> <mml:mo>→</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> , 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 $$f(T,L_m)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>T</mml:mi> <mml:mo>,</mml:mo> <mml:msub> <mm