Gamma-Ray Bursts in $1.8<z<5.6$ Suggest that the Time Variation of the Dark Energy is Small

Abstract

We calibrated the peak energy-peak luminosity relation of GRBs (so called Yonetoku relation) using 33 events with the redshift $z<1.62$ without assuming any cosmological models. The luminosity distances to GRBs are estimated from those of large amount of Type Ia supernovae with $z<1.755$. This calibrated Yonetoku relation can be used as a new cosmic distance ladder toward 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 $({\Omega }_m,{\Omega }_{\Lambda })$ plane. We obtained $({\Omega }_m,{\Omega }_{\Lambda })=(0.37_{-0.11}^{+0.14},0.63_{-0.14}^{+0.11})$ for a flat universe. Since 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 $z\sim 6$.

Comments: 4 pages, 4 figures, accepted to MNRAS