Gamma-ray Burst UV/optical afterglow polarimetry as a probe of Quantum Gravity

A possible birefringence effect that arises in quantum gravity leads to a frequency-dependent rotation of the polarization angle of linearly polarized emission from distant sources. Here we use the UV/optical polarization data of the afterglows of GRB 020813 and GRB 021004 to constrain this effect. We find an upper limit on the Gambini & Pulin birefringence parameter $| \eta | <2\times 10^{-7}$. This limit is of 3 orders better than the previous limits from observations of AGNs and of the Crab pulsar. Much stronger limits may be obtained by the future observation of polarization of the prompt $\gamma$-rays.