Probing the universe's expansion dynamics: The linear correction scenario perspective on dark energy

In this study, we investigate the cosmological evolution of the universe, focusing on the KMMS models in a model-independent approach, particularly the scenario involving linear correction, given by $E^2\left(z\right)=A\left(z\right)+\beta (1+\gamma B(z\left)\right)$, where $A\left(z\right)={\Omega }_{m0}{(1+z)}^3$ and $B\left(z\right)=z$. By analyzing recent Cosmic Chronometers (CC) and the $Pantheo{n}^{+}$ samples, we determine the best-fit values of model parameters using a Markov chain Monte Carlo analysis. Our models exhibit unique dynamics, transitioning from super-exponential to exponential expansion, with a significant shift at redshift $z_t={0.83}_{-0.10}^{+0.11}$ and present deceleration parameter $q_0=-{0.69}_{-0.17}^{+0.17}$. The jerk parameter exceeds 1, indicating a faster change in acceleration than predicted by ΛCDM. The energy density parameter is consistent with Planck observations, and the dark sector evolution follows the expected thermal history. The EoS parameter approaches ${\omega }_{de}=-1$ over time, with a current value of ${\omega }_{de0}=-1.06\pm 0.12$, aligning with the phantom phase. Our model presents a new dark energy alternative, emphasizing the importance of considering models like KMMS in understanding cosmic evolution.