Estimation of $H_0$ and $r_d$ in the $\omega(z)$ Parameterization within Einstein and Horava-Lifshitz Gravity Using DESI-Y1 and SDSS-IV

We present a novel dynamical dark energy model within the frameworks of both Einstein gravity and Horava-Lifshitz gravity. Utilizing CDMMA parametrization of the dark energy equation of state $\omega(z)$, we derive solutions to the field equations. By employing recent cosmological datasets, such as cosmic chronometer datasets, Type Ia Supernovae datasets, and Baryonic Oscillation datasets (DESI Y1 and SDSS-IV). We validate our model and determine optimal parameter values. Furthermore, we analyze the evolution of the Universe by showing the redshift dependence plots of key cosmological parameters through graphical representations. We also perform diagnostic analyses to compare our model with the standard model. Using the Akaike Information Criterion (AIC), we compare the three models and find that all of them are supported by the current data, making it impossible to discard any of them. Our model aligns well with recent observations and unveils intriguing features of the Universe, particularly the late-time behavior of the Universe.