Comparative Study of Early-Universe Epochs in an $f(R,L_m)$ Gravity Model with Effective Curvature--Matter Interaction and $\Lambda$CDM Cosmology

Abstract

We investigate a specific gravity model of the form $f(R, L_m) = \alpha R + L_m^{\beta} + \gamma$, where the nonlinear dependence on the matter Lagrangian $L_m$ introduces an effective curvature-matter interaction, leading to the non-conservation of the energy-momentum tensor. Using distance modulus data, we constrain the parameters through $\chi^2$ minimization and Bayesian MCMC analysis, obtaining statistically robust best-fit values: $H_0 = 73.75 \pm 0.16~\mathrm{km\,s^{-1}\,Mpc^{-1}}$, $\lambda = 0.262 \pm 0.007$, and $w = -0.005 \pm 0.001$. This study presents a comprehensive and statistically rigorous comparison of three key early-Universe epochs: structure formation, recombination, and matter-radiation equality between the $f(R,L_m)$ model and the standard $\Lambda$CDM cosmology. The model predicts an earlier onset of nonlinear structure formation ($z_c^{f(R,L_m)} \approx 25.6$) and a higher matter-radiation equality redshift ($z_{\mathrm{eq}}^{f(R,L_m)} \approx 4203$) compared to $\Lambda$CDM ($z_{\mathrm{eq}}^{\Lambda \mathrm{CDM}} \approx 2779$), while maintaining consistency with the observed recombination redshift ($z_{\mathrm{rec}} \approx 1092$). The recombination visibility function, derived using standard microphysical expressions with the modified expansion history, exhibits a slightly broader full width at half maximum, suggesting an extended photon decoupling period.