Constraining the Cosmological Parameters and Transition Redshift with Gamma-Ray Bursts and Supernovae

Abstract

A new method of measuring cosmology with gamma-ray bursts(GRBs) has been proposed by Liang and Zhang recently. In this method, only observable quantities including the rest frame peak energy of the νF_νspectrum (E'_p), the isotropic energy of GRB (E_{γ,iso}), and the break time of the optical afterglow light curves in the rest frame (t'_b) are used. By considering this method we constrain the cosmological parameters and the redshift at which the universe expanded from the deceleration to acceleration phase. We add five recently-detected GRBs to the sample and derive E_{γ, iso}/10^{52} ergs=(0.93\pm 0.25)\times (E'_p/100 keV)^{1.91\pm 0.32}\times (t'_b/day)^{-0.93\pm 0.38} for a flat cosmology with Ω_M=0.28 and H_0=71.0 km s^{-1} Mpc^{-1}. This relation is independent of the medium density around bursts and the efficiency of conversion of the explosion energy to gamma-ray energy that are difficult to measure. We regard the E_{γ,iso}(E'_p, t'_b) relationship as a standard candle and find 0.05<Ω_M<0.48 and Ω_Λ<1.15 (at the 1σconfidence level). In a flat universe with the cosmological constant we obtain 0.25<Ω_M <0.46 and 0.54<Ω_Λ<0.78 at the 1σconfidence level. The transition redshift is z_T=0.69_{-0.12}^{+0.11}. Combining 20 GRBs and 157 type Ia supernovae, we find Ω_M=0.29 \pm0.03 for a flat universe and the transition redshift is z_T=0.61_{-0.05}^{+0.06}, which is slightly larger than the value found by considering SNe Ia alone. In particular, We also discuss several dark-energy models in which the equation of state w(z) is arameterized and investigate constraints on the cosmological parameters in detail.

Revised version based on the referee's comments, added references, MNRAS in press