Gamma-ray bursts in 1.8 < z < 5.6 suggest that the time variation of the dark energy is small

We calibrated the peak energy-peak luminosity relation of gamma-ray bursts (GRBs; the so-called Yonetoku relation) using 33 events with redshift z < 1.62 without assuming any cosmological models. The luminosity distances to GRBs are estimated from those of large numbers of Type Ia supernovae with z < 1.755. This calibratedYonetoku relation can be used as a newcosmic distance ladder towards higher redshifts. We determined the luminosity distances of 30 GRBs in 1.8 < z < 5.6 using the calibrated relation, and plotted the likelihood contour in the (Omega(m), Omega(Lambda)) plane. We obtained (Omega(m), Omega(Lambda)) = (0.37(-0.11)(+0.14), 0.63(-0.14)(+0.11)) for a flat universe. Because our method is free from the circularity problem, we can say that our universe in 1.8 < z < 5.6 is compatible with the so-called concordance cosmological model derived for z < 1.8. This suggests that the time variation of the dark energy is small or zero up to z similar to 6.