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

TL;DR

This paper explores a modified gravity model described by a specific function of curvature and matter Lagrangian, constrains its parameters using observational data, and finds it consistent with current cosmological observations, offering an alternative to LambdaCDM.

Contribution

The paper introduces and constrains a novel f(R, L_m) gravity model using observational data, demonstrating its viability as an alternative to standard cosmology.

Findings

Best-fit H_0 = 72.77 km/s/Mpc, higher than Planck 2018 value

Model predicts transition redshift z_t rac14; 0.76 for cosmic acceleration

Bayesian analysis shows comparable support to LambdaCDM

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.