On the Gamma-Ray Burst Cosmology

Gamma-ray bursts (GRBs) are becoming more and more standardizable candles. Different methods have been proposed to measure cosmology with the relation between the γ-ray energy Eγ of a GRB jet and the peak energy Ep of the νFν spectrum in the burst frame. We compare the procedures and results of these methods. We also discuss the effects from the circumburrsrt density n and the efficiency ηγ of converting explosion energy into γ-ray emission. Using the present sample of 17 GRBs, we obtain a constraint on the mass density 0.09 < ΩM < 0.33 (1σ) for a flat ΛCDM universe with typical n ≃ 10 cm. Theoretical investigations of the Eγ ∝ E p relation reach a ∼ 1.5. The potential of GRBs for cosmology would be tested and further exerted by the plentiful observations in the Swift era. Subject headings: gamma rays: bursts — cosmology: observations—cosmology: distance scale