Testing the weak equivalence principle and Lorentz invariance with multiwavelength polarization observations of GRB optical afterglows

Violations of both the weak equivalence principle (WEP) and Lorentz invariance can produce vacuum birefringence, which leads to an energy-dependent rotation of the polarization vector of linearly polarized emission from a given astrophysical source. However, the search for the birefringent effect has been hindered by our ignorance concerning the intrinsic polarization angle in different energy bands. Considering the contributions to the observed linear polarization angle from both the intrinsic polarization angle and the rotation angles induced by violations of the WEP and Lorentz invariance, and assuming the intrinsic polarization angle is an unknown constant, we simultaneously obtain robust bounds on possible deviations from the WEP and Lorentz invariance, by directly fitting the multiwavelength polarimetric data of the optical afterglows of gamma-ray burst (GRB) 020813 and GRB 021004. Here, we show that at the $3\sigma$ confidence level, the difference of the parameterized post-Newtonian parameter $\gamma$ values characterizing the departure from the WEP is constrained to be $\Delta \gamma =(-{4.5}_{-16.0}^{+10.0})\times {10}^{-24}$ and the birefringent parameter $\eta$ quantifying the broken degree of Lorentz invariance is limited to be $\eta =\left({6.5}_{-14.0}^{+15.0}\right)\times {10}^{-7}$. These are the first simultaneous verifications of the WEP and Lorentz invariance in the photon sector. More stringent limits can be expected as the analysis presented here is applied to future multiwavelength polarization observations in the prompt gamma-ray emission of GRBs.