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This report is an update and extension of our paper accepted for publication in ApJ (arXiv:0802.4262). Since objects at the same redshift should have the same luminosity distance and the distance moduli of type Ia supernovae (SNe Ia) obtained directly from observations are completely cosmology independent, we obtain the distance modulus of a gamma-ray burst (GRB) at a given redshift by interpolating or iterating from the Hubble diagram of SNe Ia. Then we calibrate five GRB relations without assuming a particular cosmological model, from different regression methods, and construct the GRB Hubble diagram to constrain cosmological parameters. Based upon these relations we list the cosmology-independent distance moduli of 42 GRBs between redshift of 1.44 and 6.60, with the 1-$sigma$ uncertainties of 1-3%.
The unrivalled, extreme luminosities of gamma-ray bursts (GRBs) make them the favored beacons for sampling the high redshift Universe. To employ GRBs to study the cosmic terrain -- e.g., star and galaxy formation history -- GRB luminosities must be c
Apparently, Gamma-Ray Bursts (GRBs) are all but standard candles. Their emission is collimated into a cone and the received flux depends on the cone aperture angle. Fortunately we can derive the aperture angle through an achromatic steepening of the
The measure of the distances and luminosities of gamma-ray bursts (GRBs) led to the discovery that many GRB properties are strongly correlated with their intrinsic luminosity, leading to the construction of reliable luminosity indicators. These GRB l
Gamma-ray bursts (GRBs) are detectable out to very large distances and as such are potentially powerful cosmological probes. Historically, the angular distribution of GRBs provided important information about their origin and physical properties. As
Gamma Ray Bursts (GRBs) are a powerful probe of the high redshift Universe. We present a tool to estimate the detection rate of high-z GRBs by a generic detector with defined energy band and sensitivity. We base this on a population model that reprod