Cosmological test of dark energy parameterizations in Ho?ava-Lifshitz gravity

In this work, we assume that the FLRW universe, which is filled with dark matter along with dark energy, is in the framework of Horava-Lifshitz (HL) gravity. The dark energy is considered as the linear (Model I) and CPL (Model II) parameterizations of the equation of state parameter. For both models, we express the Hubble parameter H(z) in terms of the model parameters and redshift z. To rigorously constrain the model, we have employed a comprehensive set of recent observational datasets, including cosmic chronometers (CC), type Ia supernovae (SNIa), baryon acoustic oscillations (BAO), gamma-ray burst (GRB), quasar (Q) and cosmic microwave background radiation (CMB). Through the joint analysis of this diverse collection of datasets, we have achieved tighter constraints on the model's parameters. This, in turn, allows us to delve into both the physical and geometric aspects of the model with greater precision. Furthermore, our analysis has enabled us to determine the present values of crucial cosmological parameters, including H0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{0}$$\end{document}, omega m0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega _{m0}$$\end{document}, omega k0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega _{k0}$$\end{document} and omega Lambda 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega _{\Lambda 0}$$\end{document}. It is noteworthy that our results are consistent with recent findings from Planck 2018, underscoring the reliability and relevance of our models in the current cosmological context. We also conduct analysis of cosmographic parameters and apply statefinder and diagnostic tests to explore the evolution of the Universe. In addition, the statistical analysis suggests that the Lambda\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Lambda $$\end{document}CDM model is the preferred model among all our considered models. Our investigation into the models has unveiled intriguing features of the late Universe.