Viability of Big Bang Nucleosynthesis in f(R,L m) Gravity

We examine the viability of Big Bang Nucleosynthesis (BBN) constraints in f(R,L m) gravity, where the gravitational Lagrangian is an arbitrary function of the the Ricci scalar R and matter Lagrangian density L m. We derive stringent bounds on the underlying model parameters of four different f(R,L m) gravity models by examining both the primordial abundances of helium-4 (4 He) and the fractional variations in the neutron--proton freeze out temperature. Our results reveal that f(R,L m) gravity remains viable under the BBN constraints. With the freeze-out condition offering the most dominat constraint on the parameter space, whereas the bounds from 4 He abundance act as a separate abundance level consistency checks on the modified expansion rate. In summary, the presence of these feasible parameter regions demonstrates that f(R,L m) gravity models can successfully accommodate primordial element abundances without disrupting standard early Universe dynamics.