Fitting the constitution type Ia supernova data with the redshift-binned parametrization method

In this work, we explore the cosmological consequences of the recently released Constitution sample of 397 Type Ia supernovae (SNIa). By revisiting the Chevallier-Polarski-Linder (CPL) parametrization, we find that, for fitting the Constitution set alone, the behavior of dark energy (DE) significantly deviates from the cosmological constant Lambda, where the equation of state (EOS) w and the energy density rho(Lambda) of DE will rapidly decrease along with the increase of redshift z. Inspired by this clue, we separate the redshifts into different bins, and discuss the models of a constant w or a constant rho(Lambda) in each bin, respectively. It is found that for fitting the Constitution set alone, w and rho(Lambda) will also rapidly decrease along with the increase of z, which is consistent with the result of CPL model. Moreover, a step function model in which rho(Lambda) rapidly decreases at redshift z similar to 0: 331 presents a significant improvement (Delta chi(2) = -4.361) over the CPL parametrization, and performs better than other DE models. We also plot the error bars of DE density of this model, and find that this model deviates from the cosmological constant Lambda at 68.3% confidence level (CL); this may arise from some biasing systematic errors in the handling of SNIa data, or more interestingly from the nature of DE itself. In addition, for models with same number of redshift bins, a piecewise constant rho(Lambda) model always performs better than a piecewise constant w model; this shows the advantage of using rho(Lambda), instead of w, to probe the variation of DE.