Measuring dark energy with the Eiso–Ep correlation of gamma-ray bursts using model-independent methods

Abstract

We use two model-independent methods to standardize long gamma-ray bursts (GRBs) using the Eiso − Ep correlation (log Eiso = a + blog Ep), where Eiso is the isotropic-equivalent gamma-ray energy and Ep 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 σext into account and assign it to the parameter Eiso. The best-fitting values are a = 49.15 ± 0.26, b = 1.42 ± 0.11, σext = 0.34 ± 0.03 and Ωm = 0.79 in the flat ΛCDM model. The constraint on Ωm is 0.55 < Ωm< 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 Ωm = 0.50 ± 0.12. The second method uses type Ia supernovae (SNe Ia) to calibrate the Eiso − Ep 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 Ωm = 0.23+0.06-0.04 for flat ΛCDM and Ωm = 0.18 ± 0.11 and ΩΛ = 0.46 ± 0.51 for non-flat ΛCDM. For the combination of GRB and SNe Ia sample, we obtain Ωm = 0.271 ± 0.019 and h = 0.701 ± 0.002 for the flat ΛCDM and the non-flat ΛCDM, and the results are Ωm = 0.225 ± 0.044, ΩΛ = 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 Eiso − Ep correlation is promising to probe the high-redshift Universe.