Calibration of gamma-ray bursts luminosity correlations using gravitational waves as standard sirens

Gamma-ray bursts (GRBs) are a potential tool to probe high-redshift universe. However, the circularity problem enforces people to find model-independent methods to study the luminosity correlations of GRBs. Here, we present a new method which uses gravitational waves as standard sirens to calibrate GRB luminosity correlations. For the third-generation ground-based GW detectors (i.e., Einstein Telescope), the redshifts of gravitational wave (GW) events accompanied electromagnetic counterparts can reach out to $\sim 4$, which is more distant than type Ia supernovae ($z\lesssim 2$). The Amati relation and Ghirlanda relation are calibrated using mock GW catalogue from Einstein Telescope. We find that the $1\sigma$ 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 dark energy equation of state can be tightly measured, which is important for discriminating dark energy models.