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We conduct a Bayesian analysis of recent observational datasets, specificallythe Cosmic Chronometers (CC) dataset and Pantheon samples, to investigate theevolution of the EoS parameter in dark energy models. Our study focused on theeffective EoS parameter, which is described by the parametric form$\omega_{eff}=-\frac{1}{1+m(1+z)^n}$, where $m$ and $n$ are model parameters.This parametric form is applicable within the framework of $f(R,L_m)$ gravity,where $R$ represents the Ricci scalar and $L_m$ is the matter Lagrangian. Here,we examine a non-linear $f(R,L_m)$ model characterized by the functional form$f(R,L_m)=\frac{R}{2}+L_m^\alpha$, where $\alpha$ is the free parameter of themodel. We examine the evolution of several cosmological parameters, includingthe effective EoS parameter $\omega_{eff}$, the deceleration parameter $q$, thedensity parameter $\rho$, the pressure $p$, and the statefinder parameters. Ouranalysis revealed that the constrained current value of the effective EoSparameter, $\omega_{eff}^{0}=-0.68\pm0.06$ for both the CC and Pantheondatasets, points towards a quintessence phase. Moreover, at redshift $z=0$, thedeceleration parameter, $q_0 = -0.61^{+0.01}_{-0.01}$, indicates that thepresent Universe is undergoing accelerated expansion.

the european physical journal plus

Constrained evolution of effective equation of state parameter in  non-linear $f(R, L_m)$ dark energy model: Insights from Bayesian analysis of  cosmic chronometers and Pantheon samples