Gamma-ray burst contributions to constraining the evolution of dark energy

Aims. We explore the gamma-ray bursts' (GRBs') contributions in constraining the dark energy equation of state (EOS) at high (1.8 < z < 7) and at middle redshifts (0.5 < z < 1.8) and estimate how many GRBs are needed to get substantial constraints at high redshifts. Methods. We estimate the constraints with mock GRBs and mock type Ia supernovae (SNe Ia) for comparisons. When constraining the dark energy EOS in a certain redshift range, we allow the dark energy EOS parameter to vary only in that redshift bin and fix EOS parameters elsewhere to -1. Results. We find that it is difficult to constrain the dark energy EOS beyond the redshifts of SNe Ia with GRBs unless some new luminosity relations for GRBs with smaller scatters are discovered. However, at middle redshifts, GRBs have comparable contributions with SNe Ia in constraining the dark energy EOS.