We have studied the angular fluctuations in the speed of light with respect to the apex of the dipole of Cosmic Microwave Background (CMB) radiation using the experimental data obtained with GRAAL facility, located at the European Synchrotron Radiation Facility (ESRF) in Grenoble. The measurements were based on the stability of the Compton edge of laser photons scattered on the 6 GeV monochromatic electron beam. The results enable to obtain a conservative constraint on the anisotropy in the light speed variations Delta c(theta)/c < 3 10^{-12}, i.e. with higher precision than from previous experiments.
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