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 $\mathrm{Q}0405-443$, $\mathrm{Q}0347-383$, and $\mathrm{Q}0528-250$, variation in $\mu$ relative to the present day value is limited to $\Delta \mu /\mu =(2.6\pm 3.0)\times {10}^{-6}$. 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 ${\mathrm{H}}_2$ transition. Our results are consistent with no variation, and inconsistent with a previous $\approx 4\sigma$ detection of $\mu$ variation involving $\mathrm{Q}0405-443$ and $\mathrm{Q}0347-383$. 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.

Figure 1

Reduced redshift plot (${\zeta }_i$ vs $K_i$) for $\mathrm{Q}0405-443$ and $\mathrm{Q}0347-373$ with gradient $\Delta \mu /\mu =(8.5\pm 5.7)\times {10}^{-6}$ (dashed line). $\mathrm{Q}0347-373$ is represented by closed circles, and $\mathrm{Q}0405-443$ is represented by open circles. The unweighted fit, a dot-dashed line, is obscured by the weighted fit. The dotted lines give the $1\sigma$ confidence limit on the regression line. Note that this is not our preferred result, because it does not include $\mathrm{Q}0528-250$ in the fit. This graph may be compared directly with Fig. 2 of 14.