Observational data fitting to constrain Variable Modified Chaplygin Gas in the background of Horava-Lifshitz Gravity

FRW universe in Horava-Lifshitz (HL) gravity model filled with a combination of dark matter and dark energy in the form of variable modified Chaplygin gas (VMCG) is considered. The permitted values of the VMCG parameters are determined by the recent astrophysical and cosmological observational data. Here we present the Hubble parameter in terms of the observable parameters $\Omega_{dm0}$, $\Omega_{vmcg0}$, $H_{0}$, redshift $z$ and other parameters like $\alpha$, $A$, $\gamma$ and $n$. From Stern data set (12 points), we have obtained the bounds of the arbitrary parameters by minimizing the $\chi^{2}$ test. The best-fit values of the parameters are obtained by 66\%, 90\% and 99\% confidence levels. Next due to joint analysis with BAO and CMB observations, we have also obtained the bounds of the parameters ($A,\gamma$) by fixing some other parameters $\alpha$ and $n$. The best fit value of distance modulus $\mu(z)$ is obtained for the VMCG model in HL gravity, and it is concluded that our model is perfectly consistent with the union2 sample data.