Cosmological test of dark energy parametrizations within the framework of Horava-Lifshitz gravity using via Baryon Acoustic Oscillation

We are conducting an investigation to explore late-time cosmic acceleration through various dark energy parametrizations (Wettrich, Efstathiou, and Ma-Jhang) within the Horava-Lifshitz gravity framework. As an alternative to general relativity, this theory introduces anisotropic scaling at ultraviolet scales. Our primary objective is to constrain the key cosmic parameters and the Baryon Acoustic Oscillation (BAO) scale, specifically the sound horizon ($r_{d}$) by utilizing 24 uncorrelated measurements of Baryon Acoustic Oscillations (BAO) derived from recent galaxy surveys, span a redshift range from $z = 0.106$ to $z = 2.33$. Additionally, we integrate the most recent Hubble constant measurement by Riess in 2022 (denoted as R22) as an extra prior. For Wettrich, Efstathiou, and Ma-Jhang, our analysis of Baryon Acoustic Oscillation (BAO) data yields sound horizon results of $r_{d}=148.1560 \pm 2.7688 \mathrm{Mpc}$, $r_{d}=148.6168 \pm 10.2469 \mathrm{Mpc}$, and $r_{d}=147.9737 \pm 10.6096 \mathrm{Mpc}$, respectively. Incorporating the R22 prior into the BAO dataset results in $r_{d}=139.5806 \pm 3.8522 \mathrm{Mpc}$, $r_{d}=139.728025 \pm 2.7858 \mathrm{Mpc}$, and $r_{d}=139.6001 \pm 2.7441 \mathrm{Mpc}$. These outcomes highlight a distinct inconsistency between early and late observational measurements, analogous to the $H_0$ tension. A notable observation is that, when we don't include the R22 prior, the outcomes for $r_d$ tend to be in agreement with Planck and SDSS results. Following this, we conducted the Cosmography test and presented a comparative study of each parametrization with the $\Lambda$CDM paradigm. Our diagnostic analyses demonstrate that all models fit seamlessly within the phantom region. The statistical analysis indicates that neither of the two models can be ruled out based on the latest observational measurements.