Model-independent distance calibration of high-redshift gamma-ray bursts and constrain on the ΛCDM model

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Gamma-ray bursts (GRBs) are luminous enough to be detectable up to redshift z 10. They are often proposed as complementary tools to type-Ia supernovae (SNe Ia) in tracing the Hubble diagram of the Universe. The distance calibrations of GRBs usually make use one or some of the empirical luminosity correlations, such as τ lag-L, V-L, Eₚ-L, Eₚ-Eγ, τ RT-L and Eₚ-E iso relations. These calibrating methods are based on the underling assumption that the empirical luminosity correlations are universal over all redshift range. In this paper, we test the possible redshift dependence of six luminosity correlations by dividing GRBs into low-z and high-z classes according to their redshift smaller or larger than 1.4. It is shown that the Eₚ-Eγ relation for low-z GRBs is consistent with that for high-z GRBs within 1σ uncertainty. The intrinsic scatter of V-L relation is too larger to make a convincing conclusion. For the rest four correlations, however, low-z GRBs differ from high-z GRBs at more than 3σ confidence level. As such, we calibrate GRBs using the Eₚ-Eγ relation in a model-independent way. The constraint of high-z GRBs on the ΛCDM model gives Ωₘ=0.302± 0.142(1σ), well consistent with the Planck 2015 results.