Model-Independent Distance Measurements from Gamma-Ray Bursts and Constraints on Dark Energy

Gamma-Ray Bursts (GRB) are the most energetic events in the Universe, and provide a complementary probe of dark energy by allowing the measurement of cosmic expansion history that extends to redshifts greater than 6. Unlike Type Ia supernovae (SNe Ia), GRBs must be calibrated for each cosmological model considered, because of the lack of a nearby sample of GRBs for model-independent calibration. For a flat Universe with a cosmological constant, we find Omega_m=0.25^{+0.12}_{-0.11} from 69 GRBs alone. We show that the current GRB data can be summarized by a set of model-independent distance measurements, with negligible loss of information. We constrain a dark energy equation of state linear in the cosmic scale factor using these distance measurements from GRBs, together with the "Union" compilation of SNe Ia, WMAP five year observations, and the SDSS baryon acoustic oscillation scale measurement. We find that a cosmological constant is consistent with current data at 68% confidence level for a flat Universe. Our results provide a simple and robust method to incorporate GRB data in a joint analysis of cosmological data to constrain dark energy.