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We present a strong constraint on variation of the proton-to-electron mass ratio over cosmological time scales using molecular hydrogen transitions in optical quasar spectra. Using high quality spectra of quasars Q0405-443, Q0347-383, and Q0528-250, variation in relative to the present day value is limited to /= (2. 63. 0) 10^-6. We reduce systematic errors compared to previous works by substantially improving the spectral wavelength calibration method and by fitting absorption profiles to the forest of hydrogen Lyman transitions surrounding each H₂ transition. Our results are consistent with no variation, and inconsistent with a previous 4 detection of variation involving Q0405-443 and Q0347-383. If the results of this work and those suggesting that may be varying are both correct, then this would tend to disfavor certain grand unification models.
King et al. (Fri,) studied this question.