Gamma-ray bursts as standard candles to constrain the cosmological parameters

Gamma-ray bursts (GRBs) are among the most powerful sources in the Universe: they emit up to 10(54) erg in the hard x-ray band in a few tens of seconds. The cosmological origin of GRBs has been confirmed by several spectroscopic measurements of their redshifts, distributed in the range z is an element of (0.1, 6.3). These two properties make GRBs very appealing for investigating the far Universe. Indeed, they can be used to constrain the geometry of the present-day Universe and the nature and evolution of dark energy by testing the cosmological models in a redshift range hardly achievable by other cosmological probes. Moreover, the use of GRBs as cosmological tools could unveil the ionization history of the Universe, the inter-galactic medium (IGM) properties and the formation of massive stars in the early Universe. The energetics implied by the observed fluences and redshifts span at least four orders of magnitudes. Therefore, at first sight, GRBs are all but standard candles. But there are correlations among some observed quantities which allow us to know the total energy or the peak luminosity emitted by a specific burst with a great accuracy. Through these correlations, GRBs become 'known' candles, and then a new tool to constrain the cosmological parameters. One of these correlation is between the rest frame peak spectral energy E-peak and the total energy emitted in gamma-rays E-gamma, properly corrected for the collimation factor. Another correlation, discovered very recently, relates the total GRB luminosity L-iso, its peak spectral energy E-peak and a characteristic timescale T-0.45, related to the variability of the prompt emission. This last correlation is based only on prompt emission properties, it is completely phenomenological, model independent and assumption-free. These correlations have been already used to constrain Omega(M) and Omega(Lambda), which are found to be consistent with the concordance model. The present limited sample of bursts and the lack of low redshift events, necessary to calibrate the correlations used to standardize GRBs energetics, make the cosmological constraints obtained with GRBs still large compared to those obtained with other cosmological probes ( e. g. SNIa or CMB). However, the newly born field of GRB-cosmology is very promising for the future.