A New Relation between GRB Rest-Frame Spectra and Energetics and Its Utility on Cosmology

We investigate the well-measured spectral and energetic properties of 20 gamma-ray bursts (GRBs) in their cosmological rest frames. We find a tight relation between the isotropic-equivalent gamma-ray energy Eiso, the local peak energy E'p of the \nu F_{\nu} spectrum, and the local break time t'b of the GRB afterglow light curve, which reads Eiso*t'b\propto E'p^{1.95\pm0.08} (\chi^2_\nu=1.40; Omega_M=0.27, Omega_Lambda=0.73). Such a power-law relation can be understood via the high-energy radiation processes for the GRB prompt emission accompanying the beaming effects. We then consider this relation as an intrinsic one for the observed GRB sample, and obtain a constraint on the mass density Omega_M=0.24^{+0.16}_{-0.12} (1\sigma) for a flat Lambda-CDM universe, and a \chi^2_{dof}=1.33 for Omega_M\approx0.3 and Omega_Lambda\approx0.7. Ongoing GRB observations in the Swift era are expected to confirm this relation and make its cosmological utility progress much.