The Fundamental Plane of Gamma‐Ray Bursts and Its Prospect for Cosmology

We showed the independence of the $Epeak‐Lp$ from $Epeak‐Eiso$ relations, and using $Epeak,$ $Lp,$ and $Eiso$ as independent parameters, we found the fundamental plane of Gamma‐ray bursts (GRBs). The fundamental plane of GRBs is the tightest correlation only using parameters of prompt emission of GRBs. Thus this correlation have the greatest potential for cosmology among other correlations obtained from GRBs. We calibrated by distances measured by supernovae Ia (SNe Ia). Then we estimated the distance toward high redshift GRBs (z>1.8) with about 30% errors. In this talk, we present cosmological constraints from high redshift GRBs which is as strong as from type Ia supernovae (SNe Ia). Then we show the current status of GRB cosmology and compare them with SNe Ia, clusters of galaxy, and CMB cosmologies. The constraint from high redshift GRBs are consistent with others. This might indicate that the time evolution of dark energy density is not large. Finally, we discuss the future prospect of GRB cosmology.