Cosmology with gamma-ray bursts I. The Hubble diagram through the calibrated Ep,i-Eiso correlation

Context. Gamma-ray bursts (GRBs) are the most energetics explosions in the Universe. They are detectable up to very high redshifts. They may therefore be used to study the expansion rate of the Universe and to investigate the observational properties of dark energy, provided that empirical correlations between spectral and intensity properties are appropriately calibrated. Aims. We used the type Ia supernova (SN) luminosity distances to calibrate the correlation between the peak photon energy, E-p,E-i, and the isotropic equivalent radiated energy, E-iso in GRBs. With this correlation, we tested the reliability of applying these phenomena to measure cosmological parameters and to obtain indications on the basic properties and evolution of dark energy. Methods. Using 162 GRBs with measured redshifts and spectra as of the end of 2013, we applied a local regression technique to calibrate the E-p,E-i-E-iso correlation against the type Ia SN data to build a calibrated GRB Hubble diagram. We tested the possible redshift dependence of the correlation and its e ff ect on the Hubble diagram. Finally, we used the GRB Hubble diagram to investigate the dark energy equation of state (EOS). To accomplish this, we focused on the so-called Chevalier-Polarski-Linder (CPL) parametrization of the dark energy EOS and implemented the Markov chain Monte Carlo (MCMC) method to efficiently sample the space of cosmological parameters. Results. Our analysis shows once more that the E-p,E-i-E-iso correlation has no significant redshift dependence. Therefore the highredshift GRBs can be used as a cosmological tool to determine the basic cosmological parameters and to test di ff erent models of dark energy in the redshift region (z >= 3), which is unexplored by the SNIa and baryonic acoustic oscillations data. Our updated calibrated Hubble diagram of GRBs provides some marginal indication (at 1 sigma level) of an evolving dark energy EOS. A significant enlargement of the GRB sample and improvements in the accuracy of the standardization procedure is needed to confirm or reject, in combination with forthcoming measurements of other cosmological probes, this intriguing and potentially very relevant indication.