Measuring the cosmological parameters with the Ep,i-Eiso correlation of gamma-ray bursts

We have used the E-p,E-i-E-iso correlation of gamma-ray bursts (GRBs) to measure the cosmological parameter Omega(M). By adopting a maximum likelihood approach which allows us to correctly quantify the extrinsic (i.e. non- Poissonian) scatter of the correlation, we constrain (for a flat universe) Omega(M) to 0.04-0.40 (68 per cent confidence level), with a best-fitting value of Omega(M) similar to 0.15, and exclude Omega(M) = 1 at > 99.9 per cent confidence level. If we release the assumption of a flat universe, we still find evidence for a low value of Omega(M) (0.04-0.50 at 68 per cent confidence level) and a weak dependence of the dispersion of the E-p,E-i-E-iso correlation on Omega(Lambda) (with an upper limit of Omega(Lambda) similar to 1.15 at 90 per cent confidence level). Our approach makes no assumptions on the E-p,E-i-E-iso correlation and it does not use other calibrators to set the 'zero' point of the relation, therefore our treatment of the data is not affected by circularity and the results are independent of those derived via Type Ia supernovae (or other cosmological probes). Unlike other multi-parameters correlations, our analysis grounds on only two parameters, then including a larger number (a factor of similar to 3) of GRBs and being less affected by systematics. Simulations based on realistic extrapolations of ongoing (and future) GRB experiments (e.g. Swift, Konus-Wind, GLAST) show that: (i) the uncertainties on cosmological parameters can be significantly decreased and (ii) future data will allow us to get clues on the 'dark energy' evolution.