Stringent Null Constraint on Cosmological Evolution of the Proton-to-Electron Mass Ratio

We present a strong constraint on variation of the proton-to-electron mass ratio mu 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 mu relative to the present day value is limited to Delta mu/mu= (2.6 +/- 3.0) x 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 alpha transitions surrounding each H(2) transition. Our results are consistent with no variation, and inconsistent with a previous approximate to 4 sigma detection of mu variation involving Q0405 - 443 and Q0347 - 383. If the results of this work and those suggesting that alpha may be varying are both correct, then this would tend to disfavor certain grand unification models.