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

TL;DR

This paper tests a curved-space modification of gravity, $f(R,L_m)$ with $f(R,L_m)=\alpha R+L_m^{\beta}+\gamma$, as a framework for late-time cosmic acceleration. The authors derive the background dynamics, yielding $H(z)=H_0\sqrt{(1-\lambda)+\lambda(1+z)^{3(1+w)}}$ with $\lambda$ and $w$ encoding the curvature–matter coupling, and constrain $(H_0,\lambda,w)$ using a joint dataset of cosmic chronometers, Pantheon$^{+}$ SNe, DESI BAO, and CMB shift parameter via MCMC. They report best-fit values $H_0=73.75^{+0.16}_{-0.16}$ km s$^{-1}$ Mpc$^{-1}$, $\lambda=0.262^{+0.007}_{-0.007}$, and $w=-0.005^{+0.001}_{-0.001}$, predicting a transition redshift $z_t\approx0.79$ and an age $t_0\approx13.34$ Gyr, with BIC/AIC suggesting a moderate statistical preference over $\Lambda$CDM. The model provides a viable alternative to dark energy, capable of addressing the Hubble tension and offering distinctive signatures in density evolution and growth that can be tested with future precision cosmology and gravitational-wave observations.

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 - λ) + λ(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.

Figures (7)

• Figure 1: Corner plot showing the marginalized posterior distributions and parameter correlations for the $f(R,L_m)$ cosmological model obtained from the combined Hubble + SNe Ia + BAO + CMB datasets. The contours correspond to the 68% and 95% confidence regions. The parameters $(H_0, \lambda, w)$ exhibit mild degeneracies, particularly between $\lambda$ and $w$, reflecting the correlation between the effective dark-energy density and the redshift-dependent expansion rate. The posterior distributions are unimodal and approximately Gaussian, confirming good convergence of the MCMC chains. Vertical dashed lines indicate the median values and 1$\sigma$ credible intervals.
• Figure 2: Error bar plots for Hubble $H(z)$, $\mu(z)$, BAO, and CMB data. Details are described in the text. Comparison between the observational Hubble parameter measurements (points with 1$\sigma$ error bars) and the theoretical predictions from the best-fit $f(R,L_m)$ cosmological model (solid red curve). The $\Lambda$CDM prediction, which was obtained using the best-fit parameters from the Planck 2018 data (dashed blue curve), is also displayed for comparison. The $f(R,L_m)$ model accurately replicates the observed late-time expansion, matching the $\Lambda$CDM at low redshifts ($z \lesssim 1$) and exhibiting moderate deviations at higher redshifts as a result of the curvature–matter coupling. These deviations are currently within the range of current observational uncertainties, which implies that $f(R,L_m)$ gravity is a viable alternative explanation for cosmic acceleration.
• Figure 3: Deceleration parameter $q(z)$ plot for the proposed model and $\Lambda$CDM.
• Figure 4: Comparison of energy density $\rho(z)$ in the $f(R, L_m)$ model (solid red line) with the standard $\Lambda$CDM model (dashed blue line).
• Figure 5: Comparison of lookback time as a function of redshift for the modified gravity model and the $\Lambda$CDM model.