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

Abstract

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 of one or some of the empirical luminosity correlations, such as lag -L, V-L, E p -L, E p -E , RT -L and E p -E iso relations. These calibrating methods are based on the underlying 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 E p -E relation for low-z GRBs is consistent with that for high-z GRBs within 1 uncertainty. The intrinsic scatter of V-L relation is too large to make a convincing conclusion. For the rest four correlations, however, low-z GRBs differ from high-z GRBs at more than 3 confidence level. As such, we calibrate GRBs using the E p -E relation in a modelindependent way. The constraint of high-z GRBs on the cold dark matter ( CDM) model gives M = 0.302 0.142(1 ), well consistent with the Planck 2015 results.