We apply the Constitution compilation of 397 supernova Ia, the baryon acoustic oscillation measurements including the $A$ parameter, the distance ratio and the radial data, the five-year Wilkinson microwave anisotropy probe and the Hubble parameter data to study the geometry of the universe and the property of dark energy by using the popular Chevallier-Polarski-Linder and Jassal-Bagla-Padmanabhan parameterizations. We compare the simple $\chi^2$ method of joined contour estimation and the Monte Carlo Markov chain method, and find that it is necessary to make the marginalized analysis on the error estimation. The probabilities of $\Omega_k$ and $w_a$ in the Chevallier-Polarski-Linder model are skew distributions, and the marginalized $1\sigma$ errors are $\Omega_m=0.279^{ +0.015}_{ -0.008}$, $\Omega_k=0.005^{ +0.006}_{ -0.011}$, $w_0=-1.05^{ +0.23}_{ -0.06}$, and $w_a=0.5^{ +0.3}_{ -1.5}$. For the Jassal-Bagla-Padmanabhan model, the marginalized $1\sigma$ errors are $\Omega_m=0.281^{ +0.015}_{ -0.01}$, $\Omega_k=0.000^{ +0.007}_{ -0.006}$, $w_0=-0.96^{ +0.25}_{ -0.18}$, and $w_a=-0.6^{ +1.9}_{ -1.6}$. The equation of state parameter $w(z)$ of dark energy is negative in the redshift range $0\le z\le 2$ at more than $3\sigma$ level. The flat $\Lambda$CDM model is consistent with the current observational data at the $1\sigma$ level.
Categories: astro-ph.CO gr-qc hep-th