Indication of a Cosmological Variation of the Proton-Electron Mass Ratio Based on Laboratory Measurement and Reanalysis of ${\mathrm{H}}_2$ Spectra

Based on highly accurate laboratory measurements of Lyman bands of ${\mathrm{H}}_2$ and an updated representation of the structure of the ground $X{}^1\Sigma _g^{+}$ and excited $B{}^1\Sigma _u^{+}$ and $C{}^1\Pi _u$ states, a new set of sensitivity coefficients ${\mathrm{K}}_{\mathrm{i}}$ is derived for all lines in the ${\mathrm{H}}_2$ spectrum, representing the dependence of their transition wavelengths on a possible variation of the proton-electron mass ratio $\mu =m_{\mathrm{p}}/m_{\mathrm{e}}$. Included are local perturbation effects between $B$ and $C$ levels and adiabatic corrections. The new wavelengths and ${\mathrm{K}}_{\mathrm{i}}$ factors are used to compare with a recent set of highly accurate ${\mathrm{H}}_2$ spectral lines observed in the Q 0347-383 and Q 0405-443 quasars, yielding a fractional change in the mass ratio of $\Delta \mu /\mu =(2.4\pm 0.6)\times {10}^{-5}$ for a weighted fit and $\Delta \mu /\mu =(2.0\pm 0.6)\times {10}^{-5}$ for an unweighted fit. This result indicates, at a $3.5\sigma$ confidence level, that $\mu$ could have decreased in the past 12 Gyr.

Figure 1

(a) Recording of the $R(0)$ line in the $B\mathrm{\text{−}}X$ $(1,0)$ Lyman band with (b) the ${\mathrm{I}}_2$ reference spectrum and (c) étalon markers for the calibration. The line marked is the $t$-hyperfine component of the $R(46)$ line in the $B\mathrm{\text{−}}X$ $(5,5)$ band of ${\mathrm{I}}_2$ at $15259.726171{\mathrm{cm}}^{-1}$ [9].

Figure 2

Linear fit to reduced redshift of quasar absorption lines $\zeta$ as defined by Eq. (9). Solid circles: Q 0347-383, $z=3.0248970$; open circles: Q 0405-443, $z=2.5947325$. The error-weighted linear fit is shown by a dashed line, the unweighted fit by a dotted line.