Constraining Parameters of Generalized Cosmic Chaplygin Gas in Loop Quantum Cosmology

TL;DR

This paper constrains parameters of a generalized cosmic Chaplygin gas model within loop quantum cosmology using observational data, showing the model fits supernova data well and avoids future singularities.

Contribution

It provides the first detailed parameter constraints of GCCG in LQC using multiple observational datasets and analyzes the model's singularity behavior.

Findings

Best-fit parameters obtained at 66%, 90%, 99% confidence levels.

Model agrees with supernovae Type Ia data.

Model is free from future singularities.

Abstract

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.