Bayesian Statistics and Parameter Constraints on the Generalized Chaplygin Gas Model using SNe Ia Data

Abstract

The type Ia supernovae (SNe Ia) observational data are used to estimate the parameters of a cosmological model with cold dark matter and the generalized Chaplygin gas model (GCGM). The GCGM depends essentially on five parameters: the Hubble constant, the parameter $\bar{A}$ related to the velocity of the sound, the equation of state parameter $α$, the curvature of the Universe and the fraction density of the generalized Chaplygin gas (or the cold dark matter). The parameter $α$ is allowed to take negative values and to be greater than 1. The Bayesian parameter estimation yields $α= - 0.86^{+6.01}_{-0.15}$, $H_0 = 62.0^{+1.32}_{-1.42} km/Mpc.s$, $Ω_{k0}=-1.26_{-1.42}^{+1.32}$, $Ω_{m0} = 0.00^{+0.86}_{-0.00}$, $Ω_{c0} = 1.39^{+1.21}_{-1.25}$, $\bar A =1.00^{+0.00}_{-0.39}$, $t_0 = 15.3^{+4.2}_{-3.2}$ and $q_0 = -0.80^{+0.86}_{-0.62}$, where $t_0$ is the age of the Universe and $q_0$ is the value of the deceleration parameter today. Our results indicate that a Universe completely dominated by the generalized Chaplygin gas is favoured, what reinforces the idea that the this gas may unify the description for dark matter and dark energy, at least as the SNe Ia data is concerned. A closed and accelerating Universe is also favoured. The traditional Chaplygin gas model (CGM), $α= 1$ is not ruled out, even if it does not give the best-fitting. Particular cases with four or three independent free parameters are also analysed.