Constraining a $f(R, L_m)$ Gravity Cosmological Model with Observational Data

Abstract

We investigate a spatially flat FLRW cosmological model in the framework of modified gravity described by the function \( f(R, L_m) = \alpha R + L_m^\beta + \gamma \), where \( L_m \) is the matter Lagrangian density. The modified Friedmann equations yield the Hubble parameter as $ H(z) = H_0 \sqrt{(1 - \lambda) + \lambda (1 + z)^{3(1 + w)}},$ with the parameters \( \lambda = \frac{\gamma}{6\alpha H_0^2} + 1 \) and \( w = \frac{\beta(n - 2) + 1}{2\beta - 1} \). Using a Bayesian Markov Chain Monte Carlo (MCMC) approach, we constrain the model parameters with recent observational data, including cosmic chronometers, the Pantheon+ Supernovae dataset, Baryon Acoustic Oscillations (BAO), and Cosmic Microwave Background (CMB) shift parameters. The best-fit values are found to be \( H_0 = 72.773^{+0.148}_{-0.152} \) km/s/Mpc, \( \lambda = 0.289^{+0.007}_{-0.007} \), and \( w = -0.002^{+0.002}_{-0.002} \), all quoted at the 1\(\sigma\) confidence level.This model predicts a transition redshift of \( z_t \approx 0.76 \) for the onset of cosmic acceleration and an estimated universe age of 13.21 Gyr. The higher inferred value of \( H_0 \) compared to the Planck 2018 result offers a potential resolution to the Hubble tension. Additionally, using \( \rho_0 = 0.534 \times 10^{-30} \, \text{g/cm}^3 \) and assuming \( n = 1 \), we derive the model constants as \( \beta = 1.00201 \), \( \alpha = 512247 \), and \( \gamma = -1.215 \times 10^{-29} \). We also evaluate the Bayesian Information Criterion (BIC) to compare the model's performance with that of the standard \(\Lambda\)CDM model. The small BIC difference (\( \Delta \text{BIC} = 0.16 \)) indicates comparable statistical support for both models. Thus, the \( f(R, L_m) \) gravity scenario serves as a consistent and viable alternative to \(\Lambda\)CDM, potentially addressing open questions in late-time cosmology.