Constraining a f (R, L m ) Gravity Cosmological Model with Observational Data

We investigate a spatially flat FLRW cosmological model within the framework of modified gravity described by the function f (R, L m ) = αR + L β m + γ, where L m is the matter Lagrangian density. The modified Friedmann equations lead to the Hubble parameter H(z) = H 0 (1 -λ) + λ(1 + z) 3(1+w) , where λ = γ2β-1 . Using a Bayesian Markov Chain Monte Carlo (MCMC) approach, we constrain the model parameters with recent observational datasets including cosmic chronometers, Pantheon+ supernovae, baryon acoustic oscillations (BAO), and cosmic microwave background (CMB) shift parameters. The best-fit values are H 0 = 73.75 +0.16 -0.16 km s -1 Mpc -1 , λ = 0.262 ± 0.007, w = -0.005 ± 0.001, quoted at the 1σ confidence level.The model predicts a transition redshift z t ≈ 0.79 and an age of the universe of 13.34 Gyr. The inferred value of H 0 , being higher than the Planck 2018 estimate and consistent with local measurements, suggests that the model may alleviate the Hubble tension. The near-zero value of w indicates that the effective cosmic fluid behaves almost pressureless, implying that late-time acceleration is driven primarily by modified gravity effects.The Bayesian Information Criterion yields ∆BIC = -5.78, indicating positive to moderate evidence in favor of the model compared to the standard ΛCDM scenario. Therefore, the f (R, L m ) gravity framework provides a viable and consistent alternative for explaining late-time cosmic acceleration.