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Gamma-ray burst ultraviolet/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 ultraviolet/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 vertical bar eta vertical bar < 2 x 10(-7). This limit is of three orders better than the previous limits from observations of active galactic nuclei and of the Crab pulsar. Much stronger limits may be obtained by the future observation of polarization of the prompt gamma-rays.