Impact of entropy-corrected Hořava-Lifshitz gravity on modified chaplygin gas: A cosmological parameter estimation

In recent years, the search for viable alternatives to the standard $\Lambda$CDM model has intensified, particularly in light of unresolved tensions in cosmological observations and the ongoing need to better understand the nature of dark energy. In this study, we analyze the cosmological implications of the logarithmic and power-law corrected models of Hořava-Lifshitz gravity, taking modified chaplygin gas as the dark energy candidate. Using a joint chi-square minimization technique, we perform parameter estimation by fitting these models to observational data from BAO and $Pantheo{n}^{+}$ datasets. Our analysis provides best-fit values for key cosmological parameters, including the Hubble constant ($H_0$), matter density parameter (${\Omega }_{m0}$), and dark energy density parameter (${\Omega }_{\Lambda 0}$) for each model. By comparing our results with $\Lambda$CDM, we find great agreement with observational data, demonstrating that both models can serve as viable alternatives to standard cosmology. Furthermore, we evaluated our models using statistical tools such as the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) to assess their goodness of fit and complexity. After performing parameter estimation using MCMC, we studied the behavior of key cosmological parameters, including the deceleration parameter, equation of state (EoS) parameter, jerk, and snap parameters. Additionally, we analyzed various cosmological diagnostics such as the statefinder diagnostic, Om diagnostic, and $\omega -{\omega }^{\prime }$ analysis to explore the evolution of dark energy and its deviation from the standard $\Lambda$CDM model. Finally, we performed a linear perturbation analysis to study the evolution of matter fluctuations, further assessing the stability and consistency of our models with cosmological data. We also plotted $f{\sigma }_8\left(z\right)$ observational data to examine the growth rate of cosmic structures and to compare our models with large-scale structure observations. These findings suggest that entropy-corrected Hořava-Lifshitz gravity, when combined with a unified dark energy component, offer a promising framework for addressing current challenges in cosmology.