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The next Japanese X-ray Astronomy mission ASTRO-H, scheduled to be launched in 2014, will conduct the first observations with X-ray micro-calorimeter. Although it is not designed for fast follow-up, there would be chance for ToO observations of GRB afterglow to obtain a high resolution spectra that can be used to measure the absorption column density and the redshift of the GRB using absorption edges of heavy elements. We discuss the capability and scientific prospects for GRB observations with ASTRO-H. [ABSTRACT FROM AUTHOR]

We formed a GRB cosmology project in Japan, and promote the observational cosmology with Gamma-ray bursts (GRBs). In this paper, we introduce recent result of our project with the spectral Epeak-Luminosity relations. We show the Hubble diagram up to the redshift of z = 8.2, and the confidence contour of the dark energy (ΩΛ) and the dark matter (Ωm) beyond z>2 beyond the current range measured by the Type Ia supernovae. After that, we investigate the origin of data dispersion of the Epeak-brightness relations, and suggest a possible improvement of their accuracy. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We estimate a GRB formation rate based on the relation between the spectral peak energy (Ep) and the peak luminosity. This relation is derived combining the data of Ep and the peak luminosities by BeppoSAX, BATSE, HETE-2, Integral, Konus, RHESSI and Swift, and it looks considerably tighter and more reliable than the relations suggested by the previous works. In this paper, we show the revised Ep–luminosity (Yonetoku) relation. Using the new Ep–luminosity relation, we estimate redshifts of the 689 GRBs without known distances in the BATSE catalog and derive a GRB formation rate as a function of the redshift. For the redshift range of 0