Existing theory and models suggest that a Type I (merger) GRB should have a larger jet beaming angle than a Type II (collapsar) GRB, but so far no statistical evidence is available to support this suggestion. In this paper, we obtain a sample of 37 beaming angles and calculate the probability that this is true. A correction is also devised to account for the scarcity of Type I GRBs in our sample. The probability is calculated to be 83% without the correction and 71% with it.
Generalized Chaplygin gas (whose equation of state is pGCG = -A/ραGCG) was proposed as a candidate for unification of dark energy and dark matter. We investigate constraints on this model with the latest observed data. We test the model with type-Ia supernovae (SNe Ia), cosmic microwave background (CMB) anisotropy, X-ray gas mass fractions in clusters, and gamma-ray bursts (GRBs). We calibrate the GRB luminosity relations without assuming any cosmological models using SNe Ia. We show that GRBs can extend the Hubble diagram to higher redshifts (z > 6). The GRB Hubble diagram is well behaved and delineates the shape of the Hubble diagram well. We measure As ≡ A/ρα+1GCG,0 = 0.68+0.04/-0.08 (where ρGCG,0 is the energy density today) and α = -0.22+0.15-0.13 at the 1σ confidence level using all the datasets. Our results rule out the standard Chaplygin gas model (α = 1) at the 3σ confidence level. The ΛCDM is allowed at the 2σ confidence level. We find that acceleration could have started at a redshift of z ～ 0.70. The concordance of the generalized Chaplygin gas model with the age estimate of an old high redshift quasar is found. In addition, we show that GRBs can break the degeneracy between the generalized Chaplygin gas model and the XCDM model.
