A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram

Abstract

An important concern in the application of gamma-ray bursts (GRBs) to cosmology is that the calibration of GRB luminosity/energy relations depends on the cosmological model, due to the lack of a sufficient low-redshift GRB sample. In this paper, we present a new method to calibrate GRB relations in a cosmology-independent way. Since objects at the same redshift should have the same luminosity distance and since the distance moduli of Type Ia supernovae (SNe Ia) obtained directly from observations are completely cosmology independent, we obtain the distance modulus of a GRB at a given redshift by interpolating from the Hubble diagram of SNe Ia. Then we calibrate seven GRB relations without assuming a particular cosmological model and construct a GRB Hubble diagram to constrain cosmological parameters. From the 42 GRBs at $1.4<z\le 6.6$, we obtain ${\Omega }_{\mathrm{M}}=0.25_{-0.05}^{+0.04}$, ${\Omega }_{\Lambda }=0.75_{-0.04}^{+0.05}$ for the flat $\Lambda$CDM model, and for the dark energy model with a constant equation of state $w_0=-1.05_{-0.40}^{+0.27}$, which is consistent with the concordance model in a 1-$\sigma$ confidence region.

7 pages, 3 figures, 1 table, now matches the editorially revised version; accepted for publication in ApJ (vol 685);

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• Cosmology with gamma-ray bursts: II Cosmography challenges and cosmological scenarios for the accelerated Universe
• Probing the anisotropic expansion from supernovae and GRBs in a model-independent way
• Reconstructing the Cosmic Expansion History up to Redshift z=6.29 with the Calibrated Gamma-Ray Bursts
• Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach
• Revisiting Studies of the Statistical Property of a Strong Gravitational Lens System and Model-independent Constraint on the Curvature of the Universe
• Testing cosmic opacity from SNe Ia and Hubble parameter through three cosmological-model-independent methods
• Constraints on $w_0$ and $w_a$ of Dark Energy from High Redshift Gamma Ray Bursts
• Cosmological Constraints from calibrated Yonetoku and Amati relation implies Fundamental plane of Gamma-ray bursts
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• Deviation from the Cosmological Constant or Systematic Errors?
• Cosmological Models and Latest Observational Data
• Testing the interaction model with cosmological data and gamma-ray bursts
• Gamma-ray burst cosmology: Hubble diagram and star formation history
• Evolutions and Calibrations of Long Gamma-Ray Bursts Luminosity Correlations Revisited
• GRBs as standard candles: There is no "circularity problem" (and there never was)
• Cosmography by GRBs : Gamma Ray Bursts as possible distance indicators
• Observational constraints on electromagnetic Born-Infeld cosmology
• Gamma Ray Bursts -- A radio perspective
• Observational constraints from SNe Ia and Gamma-Ray Bursts on a clumpy universe
• Parameter estimation of a nonlinear magnetic universe from observations
• Constraining scalar field dark energy with cosmological observations
• Unbiased constraints on the clumpiness of universe from standard candles
• Observational constraints on the unified dark matter and dark energy model based on the quark bag model
• Testing the Consistence of Gamma Ray Burst Data-set and Supernovae Union2
• Gamma-Ray Bursts are precise distance indicators similar to Type Ia Supernovae?
• Observations of General Relativity at strong and weak limits
• GRB Cosmology and Self-organized Criticality in GRBs
• Dependence of the GRB Lag-Luminosity Relation on Redshift in the Source Frame