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 w₀ ~ -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,i, the X-ray afterglow initial luminosity L₀ and the rest-frame duration τ of the shallow phase, and the index of the late power-law decay α_X. We use it to measure Ω_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,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 Ω_M = 0.29^+0.23_-0.15 (1σ) for the ΛCDM cosmological model, and Ω_M = 0.40^+0.22_-0.16, w₀ = -1.43^+0.78_-0.66 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 Ω_m with an accuracy comparable to that exhibited by SNe Ia, and to investigate the dark energy contribution and evolution up to z ~ 10.