Estimation of \( H_0 \) and \( r_d \) in the \(\omega (z)\) parameterization within Einstein and Horava–Lifshitz gravity using DESI-Y1 and SDSS-IV

Abstract

We propose a novel dynamical dark energy model within the frameworks of Einstein gravity and Horava–Lifshitz gravity, utilizing the DCMPM parametrization of the dark energy equation of state to derive the Hubble parameter. We keep \( r_d \) as a free parameter, and use different cosmological datasets such as cosmic chronometer measurements, Type Ia Supernovae observations, and Baryon Acoustic Oscillation data from DESI Y1 and SDSS-IV to extract the posterior distributions of each model parameters. Furthermore, we investigate the evolution of the Universe using various cosmographic parameters and conduct diagnostic analyses, including the statefinder and \( O_m \) diagnostics. Using various statistical metrics, we compare both models against the standard \(\Lambda \)CDM model and find that all are well-supported by current data. Notably, the DCMPM parameterization within Einstein gravity emerges as a promising extension to the standard \(\Lambda \)CDM framework.