SIMBAD references

We present a new method aimed at handling long gamma-ray bursts (GRBs) as cosmic rulers. The recent discovery of a tight correlation between the collimation-corrected GRB energy and the peak of the gamma-ray spectrum has opened up the possibility of using GRBs as a new category of standard candles. Unfortunately, because of the lack of low-z GRBs, up to now this correlation has been obtained from high-z GRBs, with the consequence that it depends on the cosmological parameters we pretend to constrain. It is hoped that this circularity problem will be solved when, in a few years, the low-z GRB sample will be increased enough. In the meantime, we present here a new Bayesian method that eases the aforesaid circularity problem, and allows the introduction of new constraints on the cosmological (Ω_M, Ω_Λ) diagram as well as the exploration of the kinematics of the Universe up to z~ 3. The method that we propose offers the further advantage of allowing us to handle the problem of the (Ω_M, Ω_Λ) loitering line singularity which inevitably appears when standard candles with z > 2 are used. The combination of GRBs with Type Ia supernova (SN Ia) data makes the popular Λ cold dark matter (ΛCDM) cosmology more consistent with the Hubble diagram at the 68 per cent confidence level. For a flat cosmology we find Ω_M= 0.28±0.03 for the combined GRB+SN Ia data set. Correspondingly, the transition redshift between cosmic deceleration and acceleration is z_T= 0.73±0.09, slightly larger than the value found by considering SNe Ia alone. We briefly discuss our results also in terms of non-ΛCDM dark energy models.