Measuring cosmological parameters with Gamma-Ray Bursts

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In a few dozen seconds gamma ray bursts (GRBs) emit up to 10⁵4 erg in terms of an equivalent isotropically radiated energy Eiso, so they can be observed up to z 10. Thus, these phenomena appear to be very promising tools to describe the expansion rate history of the universe. Here we review the use of the Ep,i - Eiso correlation of GRBs to measure the cosmological density parameter Omegaₘ. We show that the present data set of Gamma-Ray Bursts, coupled with the assumption that we live in a flat universe, can provide independent evidence, from other probes, that Omegaₘ 0.3. We show that current (e.g., Swift, Fermi/GBM, Konus-WIND) and forthcoming GRB experiments (e.g., CALET/GBM, SVOM, Lomonosov/UFFO, LOFT/WFM) will allow us to constrain Omegaₘ with an accuracy comparable to that currently exhibited by Type Ia supernovae and to study the properties of dark energy and their evolution with time.