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 calibrated Yonetoku relation can be used as a new cosmic 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 ( m , ) plane. We obtained ( m , ) = (0.37 +0.14 −0.11 , 0.63 +0.11 −0.14 ) 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 ∼ 6.

Fluctuations of energetic radiation that seemed to be caused by a summer thunderstorm were observed at the top of Mt. Fuji. The largest of such fluctuations was gradual and lasted for about 20 minutes, and was found to be high‐energy gamma rays having a continuous energy spectrum up to 10 MeV or more. As for the feature of these fluctuations, it seems naturally that such fluctuations are caused by the bremsstrahlung photons generated by the energetic electrons produced continuously with an intense electric field in the thundercloud rather than originated in the process of lightning discharge.

We extend the Hubble diagram up to z= 5.6 using 63 gamma‐ray bursts (GRBs) via peak energy–peak luminosity relation (so‐called Yonetoku relation), and obtain constraints on cosmological parameters including dynamical dark energy parametrized by P/ρ≡w(z) =w0+wa×z/(1 +z). It is found that the current GRB data are consistent with the concordance model (Ωm= 0.28, ΩΛ= 0.72, w0=−1, wa= 0) within 2σ level. Although constraints from GRBs themselves are not so strong, they can improve the conventional constraints from type Ia supernovae because GRBs have much higher redshifts. Further, we estimate the constraints on the dark energy parameters expected by future observations with Gamma‐ray Large Area Space Telescope and Swift by Monte Carlo simulation. Constraints would improve substantially with another 150 GRBs.

We compared redshifts zY measured from the Yonetoku relation and zlag from the lag–luminosity relation for 565 BATSE gamma‐ray bursts (GRBs) and were surprised to find that the correlation between these two redshifts is very low. Assuming that the luminosity is a function of both zY and the intrinsic spectral lag τlag, we found a new redshift‐dependent lag–luminosity relation L= 7.5 × 1050 erg s−1 (1 +z)2.53τ−0.282lag with the correlation coefficient of 0.77 and the chance probability of 7.9 × 10−75. Although the spectral lag is computed from two channels of the Burst and Transient Source Experiment (BATSE), our new lag–luminosity relation suggests that a future lag–luminosity relation defined in the Swift data should also depend on the redshift.

We compared redshifts $z_Y$ from Yonetoku relation and $z_{lag}$ from the lag-luminosity relation for 565 BASTE GRBs and were surprised to find that the correlation is very low. Assuming that the luminosity is a function of both $z_Y$ and the intrinsic spectral lag $\tau_{lag}$, we found a new redshift dependent lag-luminosity relation as $L=7.5\times 10^{50}{\rm erg/s}(1+z)^{2.53}\tau_{lag}^{-0.282}$ with the correlation coefficient of 0.77 and the chance probability of $7.9\times 10^{-75}$. To check the validity of this method, we examined the other luminosity indicator, Amati relation, using $z_Y$ and the observed fluence and found the correlation coefficient of 0.92 and the chance probability of $5.2\times 10^{-106}$. Although the spectral lag is computed from two channels of BATSE, our new lag-luminosity relation suggests that a possible lag-luminosity relation in the \swift era should also depend on redshift