Observational Constraints on the Parameters of Ho\v{r}ava-Lifshitz Gravity

This study investigates the accelerated cosmic expansion within the Ho\v{r}ava-Lifshitz Model. To constrain the cosmological parameters of this model, we incorporate 17 Baryon Acoustic Oscillation points, 31 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 to extract $H_{0}$ and $r_{d}$ using late-time datasets, aiming for optimal fitting values in each model. Treating $r_{d}$ as free improves precision, reduces bias, and enhances dataset compatibility. The obtained values of $H_{0}$ and $r_{d}$ are compared to the $\Lambda$CDM model, showing consistency with previous estimates from Planck and SDSS studies. The Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) favor the Ho\v{r}ava-Lifshitz model, with the $\Lambda$CDM model having the lowest AIC. Additionally, we conduct $\Delta$AIC and $\Delta$BIC analyses to assess model preference.} Validation using the reduced $\chi_{red}^{2}$ statistic indicates satisfactory fits for the Ho\v{r}ava-Lifshitz model, while recognizing $\Lambda$CDM as the preferred model. Extensions of the analysis warrant further investigation.