2016A&A...585A..68W

We use two model-independent methods to standardize long gamma-ray bursts (GRBs) using the E_iso-E_p correlation (logE_iso=a+blogE_p), where E_ iso_ is the isotropic-equivalent gamma-ray energy and E_p is the spectral peak energy. We update 42 long GRBs and attempt to constrain the cosmological parameters. The full sample contains 151 long GRBs with redshifts from 0.0331 to 8.2. The first method is the simultaneous fitting method. We take the extrinsic scatter σ_ext into account and assign it to the parameter E_iso. The best-fitting values are a=49.15±0.26, b=1.42±0.11, σ_ext=0.34±0.03 and Ω_m=0.79 in the flat ΛCDM model. The constraint on Ω_m is 0.55<Ω_m<1 at the 1σ confidence level. If reduced χ² method is used, the best-fit results are a=48.96±0.18, b=1.52±0.08, and Ω_m=0.50±0.12. The second method uses type Ia supernovae (SNe Ia) to calibrate the E_iso-E_p correlation. We calibrate 90 high-redshift GRBs in the redshift range from 1.44 to 8.1. The cosmological constraints from these 90 GRBs are Ω_m=0.23^+0.06_–0.04 for flat ΛCDM and Ω_m=0.18±0.11 and Ω_Λ=0.46±0.51 for non-flat ΛCDM. For the combination of GRB and SNe Ia sample, we obtain Ω_m=0.271±0.019 and h=0.701±0.002 for the flat ΛCDM and the non-flat ΛCDM, and the results are Ω_m=0.225±0.044, Ω_Λ=0.640±0.082, and h=0.698±0.004. These results from calibrated GRBs are consistent with that of SNe Ia. Meanwhile, the combined data can improve cosmological constraints significantly, compared to SNe Ia alone. Our results show that the E_iso-E_p correlation is promising to probe the high-redshift Universe.