Bayesian analysis of the (generalized) Chaplygin gas and cosmological constant models using the 157 gold SNe Ia data

Abstract

The generalized Chaplygin gas model (GCGM) contains five free parameters that must be constrained using the different observational data. These parameters are: the Hubble constant H0, the parameter related to the sound velocity, the equation of state parameter α, the curvature parameter Ωk0 and the Chaplygin gas density parameter Ωc0. The pressureless matter parameter Ωm0 may be obtained as a dependent quantity. Here, these parameters are constrained through the type Ia supernovae data. The ‘gold sample’ of 157 supernovae data is used. Negative and large positive values for α are taken into account. The analysis is made by employing the Bayesian statistics and the prediction for each parameter is obtained by marginalizing on the remaining ones. This procedure leads to the following predictions: α = −0.75+4.04−0.24, H0 = 65.00+1.77−1.75, Ωk0 = −0.77+1.14−5.94, Ωm0 = 0.00+1.95−0.00, Ωc0 = 1.36+5.36−0.85, Ā = 1.000+0.000-0.534. Through the same analysis the specific case of the ordinary Chaplygin gas model (CGM), for which α = 1, is studied. In this case, there are now four free parameters and the predictions for them are: H0 = 65.01+1.81−1.71, Ωk0 = −2.73+1.53−0.97, Ωm0 = 0.00+1.22−0.00, Ωc0 = 1.34+0.94−0.70, Ā = 1.000+0.000-0.270. To complete the analysis the ΛCDM, with its three free parameters, is considered. For all these models, particular cases are considered where one or two parameters are fixed. The age of the universe, the deceleration parameter and the moment the universe begins to accelerate are also evaluated. The quartessence scenario, that unifies the description for dark matter and dark energy, is favoured. A closed (and in some cases a flat) and accelerating universe is also preferred. The CGM case α = 1 is far from been ruled out, and it is even preferred in some particular cases. In most of the cases the ΛCDM is disfavoured with respect to GCGM and CGM.