New measurements of Ωm from gamma-ray bursts

Context. Data from cosmic microwave background radiation (CMB), baryon acoustic oscillations (BAO), and supernovae Ia (SNe-Ia) support a constant dark energy equation of state with w(0) similar to -1. Measuring the evolution of w along the redshift is one of the most demanding challenges for observational cosmology. Aims. We discuss the existence of a close relation for gamma-ray bursts (GRBs), named Combo-relation, based on characteristic parameters of GRB phenomenology such as the prompt intrinsic peak energy E-p,E-i, the X-ray afterglow initial luminosity L-0 and the rest-frame duration tau of the shallow phase, and the index of the late power-law decay alpha(X). We use it to measure Omega(m) and the evolution of the dark energy equation of state. We also propose a new calibration method for the same relation, which reduces the dependence on SNe Ia systematics. Methods. We have selected a sample of GRBs with 1) a measured redshift z; 2) a determined intrinsic prompt peak energy E-p,E-i; and 3) a good coverage of the observed (0.3-10) keV afterglow light curves. The fitting technique of the rest-frame (0 : 3-10) keV luminosity light curves represents the core of the Combo-relation. We separate the early steep decay, considered a part of the prompt emission, from the X-ray afterglow additional component. Data with the largest positive residual, identified as flares, are automatically eliminated until the p-value of the fit becomes greater than 0.3. Results. We strongly minimize the dependency of the Combo-GRB calibration on SNe Ia. We also measure a small extra-Poissonian scatter of the Combo-relation, which allows us to infer from GRBs alone Omega(M) = 0.29(-0.15)(+0.23) (1 sigma) for the Lambda CDM cosmological model, and Omega(M) = 0.40(-0.16) (+0.220) ,w(0) = -1.43(-0.66)(+0.78) for the flat-Universe variable equation of state case. Conclusions. In view of the increasing size of the GRB database, thanks to future missions, the Combo-relation is a promising tool for measuring Omega(m) with an accuracy comparable to that exhibited by SNe Ia, and to investigate the dark energy contribution and evolution up to z similar to 10.