New measurements of \(\Omega_m\) 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 \(w_0 \sim -1\). 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 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, the initial luminosity of the shallow phase \(L_0\), 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 \(E_{p,i}\), and 3) a good coverage (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 \(\Omega_M =0.29^{+0.23}_{-0.15}\) (1\(\sigma\)) for the \(\Lambda\)CDM cosmological model, and \(\Omega_M =0.40^{+0.22}_{-0.16}\), \(w_0 = -1.43^{+0.78}_{-0.66}\) for the flat-Universe variable equation of state case.