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 one. 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} = 0.74_{1.32}^{+1.42}, 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 favored, which reinforces the idea that the this gas may unify the description for dark matter and dark energy, at least as far as the SNe Ia data is concerned. A closed and accelerating Universe is also favored. The traditional Chaplygin gas model (CGM), α = 1 is not ruled out, even if it does not give the bestfitting. Particular cases with four or three independent free parameters are also analyzed.
 Publication:

International Journal of Modern Physics D
 Pub Date:
 DOI:
 10.1142/S0218271805006729
 arXiv:
 arXiv:astroph/0409245
 Bibcode:
 2005IJMPD..14..775C
 Keywords:

 98.80.Bp;
 98.80.Es;
 04.60.Gw;
 Origin and formation of the Universe;
 Observational cosmology;
 Covariant and sumoverhistories quantization;
 Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 18 pages, LaTeX 2e, 2 tables, 20 EPS figures, uses graphicx