Bayesian Analysis of the (Generalized) Chaplygin Gas and Cosmological Constant Models using the 157 gold SNe Ia Data

The generalized Chaplygin gas model (GCGM) contains 5 free parameters, here, they are constrained through the type Ia supernovae data, i.e., the ``gold sample'' of 157 supernovae data. Negative and large positive values for $\alpha$ 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 remained ones. This procedure leads to the following predictions: $\alpha = - 0.75^{+4.04}_{-0.24}$, $H_0=65.00^{+1.77}_{-1.75}$, $\Omega_{k0} = - 0.77^{+1.14}_{-5.94}$, $\Omega_{m0} = 0.00^{+1.95}_{-0.00}$, $\Omega_{c0} = 1.36^{+5.36}_{-0.85}$, $\bar A = 1.000^{+0.000}_{-0.534}$. Through the same analysis the specific case of the ordinary Chaplygin gas model (CGM), for which $\alpha = 1$, is studied. In this case, there are now four free parameters and the predictions for them are: $H_0 = 65.01^{+1.81}_{-1.71}$, $\Omega_{k0} = - 2.73^{+1.53}_{-0.97}$, $\Omega_{m0} = 0.00^{+1.22}_{-0.00}$, $\Omega_{c0} = 1.34^{+0.94}_{-0.70}$, $\bar A = 1.000^{+0.000}_{-0.270}$. To complete the analysis the $\Lambda$CDM, 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, is favoured. A closed (and in some cases a flat) and accelerating Universe is also preferred. The CGM case $\alpha = 1$ is far from been ruled out, and it is even preferred in some particular cases. In most of the cases the $\Lambda$CDM is disfavoured with respect to GCGM and CGM.Comment: 23 pages, LaTeX 2e, 6 tables, 38 EPS figures, uses graphic

On the consistency of a repulsive gravity phase in the early Universe

We exploit the possibility of existence of a repulsive gravity phase in the evolution of the Universe. A toy model with a free scalar field minimally coupled to gravity, but with the "wrong sign" for the energy and negative curvature for the spatial section, is studied in detail. The background solutions display a bouncing, non-singular Universe. The model is well-behaved with respect to tensor perturbations. But, it exhibits growing models with respect to scalar perturbations whose maximum occurs in the bouncing. Hence, large inhomogeneties are produced. At least for this case, a repulsive phase may destroy homogeneity, and in this sense it may be unstable. A newtonian analogous model is worked out; it displays qualitatively the same behaviour. The generality of this result is discussed. In particular, it is shown that the addition of an attractive radiative fluid does not change essentially the results. We discuss also a quantum version of the classical repulsive phase, through the Wheeler-de Witt equation in mini-superspace, and we show that it displays essentially the same scenario as the corresponding attractive phase.Comment: Latex file, 15 pages, 7 figures. There is a new figure, a new section and some other minor correction

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

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 $\alpha$, the curvature of the Universe and the fraction density of the generalized Chaplygin gas (or the cold dark matter). The parameter $\alpha$ is allowed to take negative values and to be greater than 1. The Bayesian parameter estimation yields $\alpha = - 0.86^{+6.01}_{-0.15}$, $H_0 = 62.0^{+1.32}_{-1.42} km/Mpc.s$, $\Omega _{k0}=-1.26_{-1.42}^{+1.32}$, $\Omega_{m0} = 0.00^{+0.86}_{-0.00}$, $\Omega_{c0} = 1.39^{+1.21}_{-1.25}$, $\bar A =1.00^{+0.00}_{-0.39}$, $t_0 = 15.3^{+4.2}_{-3.2}$ 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), $\alpha = 1$ 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.Comment: 18 pages, LaTeX 2e, 2 tables, 20 EPS figures, uses graphic

Bayesian Analysis of the Chaplygin Gas and Cosmological Constant Models using the SNe Ia Data

The type Ia supernovae observational data are used to estimate the parameters of a cosmological model with cold dark matter and the Chaplygin gas. The Chaplygin gas model depends essentially on four parameters: the Hubble constant, the velocity of the sound of the Chaplygin gas, the curvature of the Universe and the fraction density of the Chaplygin gas and the cold dark matter. The Bayesian parameter estimation yields $H_0 = 62.1^{+3.3}_{-3.4} km/Mpc.s$, $\Omega_{k0} = -0.84^{+1.51}_{-1.23}$, $\Omega_{m0} = 0.0^{+0.82}_{-0.0}$, $$, $\bar{A} = c_s^2 = 0.93^{+0.07}_{-0.21} c$, $t_0 = 14.2^{+2.8}_{-1.3} Gy$ and $q_0 = - 0.98^{+1.02}_{-0.62}$. These and other results indicate that a Universe completely dominated by the Chaplygin gas is favoured, at least as the type Ia supernovae data are concerned. A closed and accelerating Universe is also favoured. The Bayesian statistics indicates that the Chaplygin gas model is more likely than the standard cosmological constant ($\Lambda CDM$) model at 55.3% confidence level when an integration on all free parameters is performed. Assuming the spatially flat curvature, this percentage mounts to 65.3%. On the other hand, if the density of dark matter is fixed at zero value, the Chaplygin gas model becomes more preferred than the $\Lambda CDM$ model at 91.8% confidence level. Finally, the hypothesis of flat Universe and baryonic matter ($\Omega_{b0}=0.04$) implies a Chaplygin gas model preferred over the $\Lambda CDM$ at a confidence level of 99.4%.Comment: 19 pages, LaTeX 2e, 4 EPS figures, uses graphic