  This study investigates accelerated cosmic expansion using various
cosmological models within Horava-Lifshitz gravity, including BBCCFHKO, Seljak,
ASSS, PADE-I, PADE-II, and BAZS, utilizing Equation of State Parametrization.
To constrain the cosmological parameters of each model, we incorporate 24
Baryon Acoustic Oscillation points, 30 Cosmic Chronometer points, 40 Type Ia
Supernovae points, 24 quasar Hubble diagram points, and 162 Gamma Ray Bursts
points, along with the latest Hubble constant measurement (R22). We treat
$r_{d}$ as a free parameter, aiming to extract $H_{0}$ and $r_{d}$ using
late-time datasets and obtain optimal fitting values for each parameter in
every model. The benefits of treating $r_{d}$ as a free parameter include
reduced bias, improved precision, and enhanced dataset compatibility. The
resulting values of $H_{0}$ and $r_{d}$ are relative to the $\Lambda$CDM model,
showcasing alignment with early Planck and SDSS estimations. We additionally
minimize errors by simulating random correlations in the covariance matrix.
Furthermore, the Akaike Information Criterion (AIC) and Bayesian Information
Criterion (BIC) support all models, with the $\Lambda$CDM model exhibiting the
lowest AIC. Evaluation via reduced chi-square statistic confirms reasonable
fits for all models. While $\Lambda$CDM remains favored, extensions warrant
further investigation. This study underscores the importance of exploring
alternative cosmological models to deepen our understanding of the universe's
fundamental properties and evolution. Continued refinement of models is
essential for advancing cosmological research.
