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 Λ, where the equation of state (EOS) w and the energy density ρ_Λ 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 ρ_Λ in each bin, respectively. It is found that for fitting the Constitution set alone, w and ρ_Λ 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 ρ_Λ rapidly decreases at redshift z~0.331 presents a significant improvement (Δχ²=-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 Λ 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 ρ_Λ model always performs better than a piecewise constant w model; this shows the advantage of using ρ_Λ, instead of w, to probe the variation of DE.