Exploring Late-Time Cosmic Acceleration with Eos Parameterizations in Horava-Lifshitz Gravity via Baryon Acoustic Oscillations

In this study, the framework of Horava-Lifshitz gravity to model the Universe's dark matter and dark energy (DE) components is adopted. Specifically, two recent parametrizations for DE models: the CBDRM-type and CADMM-type parameterizations is considered. In the analysis, the Hubble parameter is explicitly expressed, denoted as H(z)$H(z)$, for these two distinct dark energy models. By doing so, investigate and quantify the accelerated cosmic expansion rate characterizing the late-time Universe is aimed. This study uses a wide range of datasets. This dataset consists of recent measurements of baryon acoustic oscillations (BAOs) collected over a period of 22 years with the Cosmic Chronometers (CC) dataset, Type Ia supernovae (SNIa) dataset, the Hubble diagram of gamma-ray bursts (GRBs), quasars (Q), and the latest measurement of the Hubble constant (R22). Consequently, a crucial aspect of this study by plotting the rd$r_{d}$ vs. H0 plane is presented. In the context of the Lambda CDM model, after incorporating all the datasets, including the R22 prior, the following results: H0 = 71.674089 +/- 0.734089 kms-1Mpc-1$km s<^>{-1} Mpc<^>{-1}$ and rd=143.050380Mpc +/- 3.702038$r_d = 143.050380 Mpc \pm 3.702038$ is obtained. For the CBDRM model, H0 = 72.355058 +/- 1.004604 kms-1Mpc-1$km s<^>{-1} Mpc<^>{-1}$ and rd=144.835069Mpc +/- 2.378848$r_d = 144.835069 Mpc \pm 2.378848$ is found. In the case of the CADMM model, the analysis yields H0 = 72.347804 +/- 0.923328 kms-1Mpc-1$km s<^>{-1} Mpc<^>{-1}$ and rd=144.466836Mpc +/- 4.288758$r_d = 144.466836 Mpc \pm 4.288758$. Cosmographic analyses for both of the proposed parameterizations in comparison to the Lambda CDM paradigm are conducted. Additionally, Diagnostic tests to investigate the evolution of both models is applied. Finally, the Information Criteria test demonstrates that the Lambda CDM model emerges as the preferred choice among the models is considered.