SIMBAD references

Gamma-ray bursts (GRBs) are a potential tool to probe the high-redshift universe. However, the circularity problem has encouraged people to find model-independent methods to study the luminosity correlations of GRBs. Here, we present a new method that uses gravitational waves (GWs) as standard sirens to calibrate GRB luminosity correlations. For the third-generation ground-based GW detectors (i.e., Einstein Telescope-ET), the redshifts of GW events accompanying electromagnetic counterparts can reach out to ∼4, which is more distant than type Ia supernovae (z <= 2). The Amati relation and Ghirlanda relation are calibrated using the mock GW catalog from ET. We find that the 1σ uncertainty of intercepts and slopes of these correlations can be constrained to less than 0.2% and 8% respectively. Using calibrated correlations, the evolution of the dark energy equation of state can be tightly measured, which is important for discriminating dark energy models.