A Modified Generalized Chaplygin Gas as the Unified Dark Matter-Dark Energy Revisited

A modified generalized Chaplygin gas (MGCG) is considered as the unified dark matter-dark energy revisited. The character of MGCG is endued with the dual role, which behaves as matter at early times and as an quiessence dark energy at late times. The equation of state for MGCG is $p=-\alpha\rho/(1+\alpha)-\vartheta(z)\rho^{-\alpha}/(1+\alpha)$, where $\vartheta(z)=-[\rho_{0c}(1+z)^{3}]^{(1+\alpha)}(1-\Omega_{0B})^{\alpha}\{\alpha\Omega_{0DM}+ \Omega_{0DE}[\omega_{DE}+\alpha(1+\omega_{DE})](1+z)^{3\omega_{DE}(1+\alpha)}\}$. Some cosmological quantities, such as the densities of different components of the universe $\Omega_{i}$ ($i$ respectively denotes baryons, dark matter and dark energy) and the deceleration parameter $q$, are obtained. The present deceleration parameter $q_{0}$, the transition redshift $z_{T}$ and the redshift $z_{eq}$, which describes the epoch when the densities in dark matter and dark energy are equal, are also calculated. To distinguish MGCG from others, we then apply the Statefinder diagnostic. Later on, the parameters ($\alpha$ and $\omega_{DE}$) of MGCG are constrained by combination of the sound speed $c^{2}_{s}$, the age of the universe $t_{0}$, the growth factor $m$ and the bias parameter $b$. It yields $\alpha=-3.07^{+5.66}_{-4.98}\times10^{-2}$ and $\omega_{DE}=-1.05^{+0.06}_{-0.11}$. Through the analysis of the growth of density perturbations for MGCG, it is found that the energy will transfer from dark matter to dark energy which reach equal at $z_{eq}\sim 0.48$ and the density fluctuations start deviating from the linear behavior at $z\sim 0.25$ caused by the dominance of dark energy.