Model-independent parameterization of H(z) and its implications for cosmic evolution

We investigate the model-independent parameterization of $H\left(z\right)$ in spatially homogeneous and isotropic FLRW space-time using Cosmic Chronometers (31 data points) and Pantheon+SH0ES (1701 points) datasets. The best-fit values for the model parameters $(H_0,A_1,A_2,A_3)$ are obtained through MCMC analysis. Our results show that the EoS parameter ω transitions from a matter-dominated era through quintessence to $\omega =-1$, indicating convergence to ΛCDM at late times. The current ω values suggest an accelerating universe. Moreover, the model's squared sound speed $v_s^2$ evolves from negative to positive, indicating increasing stability. The deceleration parameter q shows a smooth transition from deceleration to acceleration, with transition redshift $z_t$ between 0.5 and 0.8. Further, the energy conditions are satisfied, and SEC violation at $z=0$ supports current acceleration. The $\omega -{\omega }^{\prime }$ plane lies in the freezing region, and the $r-s$ plane approaches the ΛCDM limit at late times.