Long Gamma-Ray Burst prompt emission properties as a cosmological tool

Recently we discovered a tight correlation among quantities that characterize the prompt gamma-ray emission of long GRBs with known redshifts (Firmani et al. 2006). Studying how this correlation changes for different cosmological parameters, we find that its scatter is minimum for the concordance cosmology. Encouraged by this coincidence we present the first cosmological constraints obtained by using this multi variable correlation, based on a sample of 19 GRBs in the redshift range of 0.17--4.5. To circumvent the problem that the correlation depends on the cosmological parameters that we pretend to constrain, we apply the Bayesian-like method presented in a previous paper. Our results are fully consistent with the cosmological constant (Lambda) cosmology, in particular with the flat geometry case. Assuming the Lambda cosmology, we find Omega_m=0.31^{+0.09}_{-0.08} and Omega_L=0.80^{+0.20}_{-0.30} (1sigma). Assuming further flat geometry, we find Omega_m=0.29^{+0.08}_{-0.06} (1sigma). Based on our low--number GRB sample alone, it is difficult to give accurate constraints on the evolution of the dark energy equation of state. However, the concordance-cosmology case (equation of state parameter constant and equal to -1) is consistent at the 68.3% CL with the GRB constraints. The optimal approach to improve the constraints on dynamical cosmological parameters would be to combine both GRBs and type-Ia supernova data in the same analysis with the Hubble-diagram method