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.
Comment: 10 pages, 9 figures, 3 tables. Accepted for publication in A&A. Truncated abstract text