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

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.

💡 Research Summary

The paper investigates a spatially flat Friedmann‑Lemaître‑Robertson‑Walker (FLRW) cosmology within the modified gravity framework f(R, L_m), where the gravitational action depends on both the Ricci scalar R and the matter Lagrangian density L_m. The authors adopt a specific functional form f(R, L_m)=αR+L_m^β+γ, with three free parameters (α, β, γ). By varying the action, they derive the modified field equations, which simplify considerably because f_R=α is constant. Assuming L_m=ρ (the matter energy density) and a perfect fluid with equation of state p=(1−n)ρ, they obtain two modified Friedmann equations. Solving these equations yields a first‑order linear differential equation for H(z)^2, whose solution can be expressed compactly after introducing two dimensionless parameters: λ ≡ 1+γ/(6αH_0^2) and w ≡