Testing weak equivalence principle with strongly lensed cosmic transients

Current constraints on Einstein’s weak equivalence principle (WEP) utilize the observed time delay between correlated particles of astronomical sources. However, the intrinsic time delay due to particle emission time and the time delays caused by potential Lorentz-invariance violation and non-zero rest mass of photons were simply omitted in previous studies. Here we propose a robust method to test WEP using strongly lensed cosmic transients, which can naturally overcome these time delays. This can be achieved by comparing the time delays between lensed images seen in different energy bands or in gravitational waves (GWs) and their electromagnetic (EM) counterparts. The power of our method mainly depends on the timing accuracy of cosmic transient and the strong lensing time delay. If the time delay of cosmic transient can be measured with accuracy about 0.1 s (e.g. gamma-ray bursts), we show that the upper limit on the differences of the parameterized post-Newtonian parameter $$\gamma $$ value is $$\varDelta \gamma