Constraining the evolution of dark energy with type Ia supernovae and   gamma-ray bursts
  The behavior of the dark energy equation of state (EOS) is crucial in distinguishing different cosmological models. With a model independent approach, we constrain the possible evolution of the dark energy EOS. Gamma-ray bursts (GRBs) of redshifts up to $z>6$ are used, in addition to type Ia supernovae (SNe Ia). We separate the redshifts into 4 bins and assume a constant EOS parameter for dark energy in each bin. The EOS parameters are decorrelated by diagonalizing the covariance matrix. And the evolution of dark energy is estimated out of the uncorrelated EOS parameters. By including GRB luminosity data, we significantly reduce the confidence interval of the uncorrelated EOS parameter whose contribution mostly comes from the redshift bin of $0.5<z<1.8$. At high redshift where we only have GRBs, the constraints on the dark energy EOS are still very weak. However, we can see an obvious cut at about zero in the probability plot of the EOS parameter, from which we can infer that the ratio of dark energy to matter most probably continues to decrease beyond redshift 1.8. We carried out analyses with and without including the latest BAO measurements, which themselves favor a dark energy EOS of $w<-1$. If they are included, the results show some evidence of an evolving dark energy EOS. If not included, however, the results are consistent with the cosmological constant within $1 \sigma$ for redshift $0<z \lesssim 0.5$ and $2 \sigma$ for $0.5 \lesssim z<1.8$. 
Shi Qi, Fa-Yin Wang, and Tan Lu