Constraining Parameters of Generalized Cosmic Chaplygin Gas in Loop
  Quantum Cosmology
  We have assumed the FRW universe in loop quantum cosmology (LQC) model filled
with the dark matter and the Generalized Cosmic Chaplygin gas (GCCG) type dark
energy where dark matter follows the linear equation of state. We present the
Hubble parameter in terms of the observable parameters $\Omega_{m0}$ and
$H_{0}$ with the redshift $z$ and the other parameters like $A$, $B$, $w_{m}$,
$ \omega$ and $\alpha$ which coming from our model. From Stern data set (12
points)\& SNe Type Ia 292 data (from \cite{Riess1,Riess2,Astier}) 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 Stern+BAO and Stern+BAO+CMB
observations, we have also obtained the bounds of the parameters ($A,B$) by
fixing some other parameters $\alpha$, $w_{m}$ and $\omega$. From the best fit
values of the parameters, we have obtained the distance modulus $\mu(z)$ for
our theoretical GCCG model in LQC and from Supernovae Type Ia (union2 sample
552 data from [\cite{Amanullah}] \& Riess 292 data from
[\cite{Riess1,Riess2,Astier}]), we have concluded that our model is in
agreement with the Supernovae Type Ia sample data. In addition, we have
investigated in details about the various types of Future Singularities that
may be formed in this model and it is notable that our model is completely free
from any types of future singularities.
