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 \( f(R, L_m) = αR + L_m^β+ γ\), where \( L_m \) is the matter Lagrangian density. The modified Friedmann equations yield the Hubble parameter as $H(z)=H_0\sqrt{(1-\hat{I}»)+\hat{I}»(1+z{)}^{3(1+w)}},$ with the parameters \( λ= \fracγ{6αH_0^2} + 1 \) and \( w = \frac{β(n - 2) + 1}{2β- 1} \). 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, \( λ= 0.289^{+0.007}_{-0.007} \), and \( w = -0.002^{+0.002}_{-0.002} \), all quoted at the 1\(σ\) 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 \( ρ_0 = 0.534 \times 10^{-30} \, \text{g/cm}^3 \) and assuming \( n = 1 \), we derive the model constants as \( β= 1.00201 \), \( α= 512247 \), and \( γ= -1.215 \times 10^{-29} \). We also evaluate the Bayesian Information Criterion (BIC) to compare the model's performance with that of the standard \(Λ\)CDM model. The small BIC difference (\( Δ\text{BIC} = 0.16 \)) indicates comparable statistical support for both models. Thus, the \( f(R, L_m) \) gravity scenario serves as a consistent and viable alternative to \(Λ\)CDM, potentially addressing open questions in late-time cosmology.

20 pages,5figures