Exploring the Latest Union2 SNIa Dataset by Using Model-Independent
  Parametrization Methods
  We explore the cosmological consequences of the recently released Union2
sample of 557 Type Ia supernovae (SNIa). Combining this latest SNIa dataset
with the Cosmic microwave background (CMB) anisotropy data from the Wilkinson
Microwave Anisotropy Probe 7 year (WMAP7) observations and the baryon acoustic
oscillation (BAO) results from the Sloan Digital Sky Survey (SDSS) Data Release
7 (DR7), we measure the dark energy density function $f(z)\equiv
\rho_{de}(z)/\rho_{de}(0)$ 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 advantage in fitting
observational data than 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 SNIa dataset, which more
favors a dynamical dark energy.
