Testing the Einstein's equivalence principle with polarized gamma-ray bursts

The Einstein's equivalence principle can be tested by using parameterized post-Newtonian parameters, of which the parameter $\gamma$ has been constrained by comparing the arrival times of photons with different energies. It has been constrained by a variety of astronomical transient events, such as gamma-ray bursts (GRBs), fast radio bursts as well as pulses of pulsars, with the most stringent constraint of $\Delta \gamma \lesssim 10^{-15}$. In this letter, we consider the arrival times of lights with different circular polarization. For a linearly polarized light, it is the combination of two circularly polarized lights. If the arrival time difference between the two circularly polarized lights is too large, their combination may lose the linear polarization. We constrain the value of $\Delta \gamma_{\rm p} < 1.6 \times 10^{-27}$ by the measurement of the polarization of GRB 110721A, which is the most stringent constraint ever achieved.