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We have used the   E  p, i  – E  iso   correlation of gamma‐ray bursts (GRBs) to measure the cosmological parameter Ω 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) Ω M  to 0.04–0.40 (68 per cent confidence level), with a best‐fitting value of  Ω M ∼ 0.15 , and exclude  Ω M = 1  at &gt;99.9 per cent confidence level. If we release the assumption of a flat universe, we still find evidence for a low value of Ω M  (0.04–0.50 at 68 per cent confidence level) and a weak dependence of the dispersion of the   E  p, i  – E  iso   correlation on  Ω Λ   (with an upper limit of  Ω Λ ∼ 1.15  at 90 per cent confidence level). Our approach makes no assumptions on the   E  p, 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 ∼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.

Measuring the cosmological parameters with the E p, i – E iso correlation of gamma‐ray bursts