Exploring the latest Union2 type Ia supernovae dataset by using model-independent parametrization methods

We explore the cosmological consequences of the recently released Union2 sample of 557 type Ia supernovae. Combining this latest type Ia supernovae dataset with the cosmic microwave background anisotropy data from the Wilkinson Microwave Anisotropy Probe 7-yr observations and the baryon acoustic oscillation results from the Sloan Digital Sky Survey data release 7, we measure the dark energy density function f(z) equivalent to rho(de)(z)/rho(de)(0) as a free function of redshift. Two model-independent parametrization methods (the binned parametrization and the polynomial interpolation parametrization) are used in this paper. By using the chi(2) statistic and the Bayesian information criterion, we find that the current observational data are still too limited to distinguish which parametrization method is better, and a simple model has the advantage in fitting observational data over a complicated model. Moreover, it is found that all these parametrizations demonstrate that the Union2 dataset is still consistent with a cosmological constant at 1 sigma confidence level. Therefore, the Union2 dataset is different from the Constitution type Ia supernovae dataset, which more favors a dynamical dark energy.