Observational Constraints of Modified Chaplygin Gas in Loop Quantum Cosmology

Abstract

We have considered the FRW universe in loop quantum cosmology (LQC) model filled with the dark matter (perfect fluid with negligible pressure) and the modified Chaplygin gas (MCG) type dark energy. We present the Hubble parameter in terms of the observable parameters $\Omega_{m0}$, $\Omega_{x0}$ and $H_{0}$ with the redshift $z$ and the other parameters like $A$, $B$, $C$ and $\alpha$. 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 ($B,C$) by fixing some other parameters $\alpha$ and $A$. From the best fit of distance modulus $\mu(z)$ for our theoretical MCG model in LQC, we concluded that our model is in agreement with the union2 sample data.