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

We have used the Ep,i-Eiso correlation of gamma-ray bursts (GRBs) to measure the cosmological parameter ΩM. 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) ΩM to 0.04-0.40 (68 per cent confidence level), with a best-fitting value of ΩM ~ 0.15, and exclude ΩM = 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 ΩM (0.04-0.50 at 68 per cent confidence level) and a weak dependence of the dispersion of the Ep,i-Eiso correlation on ΩΛ (with an upper limit of ΩΛ ~ 1.15 at 90 per cent confidence level). Our approach makes no assumptions on the Ep,i-Eiso 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 ~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