Abstract
Recently, a tight correlation among three quantities that characterize the prompt emission of long Gamma-Ray Bursts (GRBs) with known redshift z, was discovered (Firmani et al. 2006a). We use this correlation to construct the Hubble diagram (HD) with a sample of 19 GRBs in the broad range of z = 0.17 - 4.5, and carry out a full statistical analysis to constrain cosmological parameters (CPs). To optimally solve the problem of circularity, a Bayesian approach is applied. The main result is that the concordance ΛCDM cosmology is fully consistent with the GRB data at the level of several tests. If we assume the Λ cosmology, then we find Ω=0.31^{+0.09}-0.08 and OL=0.80^{+0.20}-0.30 (1σ); the flat-geometry case is within 1σ. Assuming flatness, we find Ω=0.29^{+0.08}-0.06, and fixing Ω=0.28, we obtain a dark energy equation of state parameter w=-1.07^{+0.25}-0.38, i.e. the ΛCDM model (w=-1) is within 1σ. Given the low number of usable GRBs we cannot yet constrain well the possible evolution of w = w(z). However, the case w(z)=-1 (ΛCDM) is consistent at the 68.3% CL with GRBs. It is shown also how a broad range of z's in the used sample improves the determination of CPs from the HD, which is the case of GRBs as distance indicators.
