An updated Gamma Ray Bursts Hubble diagram

TL;DR

This paper updates the Gamma Ray Bursts Hubble diagram by incorporating new correlations, a Bayesian calibration method, and a model-independent calibration approach, resulting in a larger and more robust dataset for cosmological analysis.

Contribution

It introduces a new calibration procedure for GRB correlations using local regression on supernova data, reducing dependence on cosmological models.

Findings

Expanded GRB sample to 83 objects with updated correlations.

Demonstrated the impact of different cosmological parameters on mu(z).

Provided a nearly model-independent GRB Hubble diagram with 69 GRBs.

Abstract

Gamma ray bursts (GRBs) have recently attracted much attention as a possible way to extend the Hubble diagram to very high redshift. To this aim, the luminosity (or isotropic emitted energy) of a GRB at redshift z must be evaluated from a correlation with a distance independent quantity so that one can then solve for the luminosity distance D_L(z) and hence the distance modulus mu(z). Averaging over five different two parameters correlations and using a fiducial cosmological model to calibrate them, Schaefer (2007) has compiled a sample of 69 GRBs with measured mu(z) which has since then been widely used to constrain cosmological parameters. We update here that sample by many aspects. First, we add a recently found correlation for the X - ray afterglow and use a Bayesian inspired fitting method to calibrate the different GRBs correlations known insofar assuming a fiducial LCDM model in agreement with the recent WMAP5 data. Averaging over six correlations, we end with a new GRBs Hubble diagram comprising 83 objects. We also extensively explore the impact of varying the fiducial cosmological model considering how the estimated mu(z) change as a function of the $(\Omega_M, w_0, w_a)$ parameters of the Chevallier - Polarski - Linder phenomenological dark energy equation of state. In order to avoid the need of assuming an {\it a priori} cosmological model, we present a new calibration procedure based on a model independent local regression estimate of mu(z) using the Union SNeIa sample to calibrate the GRBs correlations. This finally gives us a GRBs Hubble diagram made out of 69 GRBs whose estimated distance modulus mu(z) is almost independent on the underlying cosmological model.