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 μ 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 μ relative to the present day value is limited to Δμ/μ=(2.6±3.0)×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 α transitions surrounding each H₂ transition. Our results are consistent with no variation, and inconsistent with a previous ≈4σ detection of μ variation involving Q0405-443 and Q0347-383. If the results of this work and those suggesting that α may be varying are both correct, then this would tend to disfavor certain grand unification models.