Highly AccurateH2Lyman and Werner Band Laboratory Measurements and an Improved Constraint on a Cosmological Variation of the Proton-to-Electron Mass Ratio

Transition wavelengths on a large set of ${\mathrm{H}}_2$ Lyman and Werner band spectral lines have been obtained at an accuracy of $5\times {10}^{-8}$, using a narrow band tunable extreme ultraviolet laser. The data are used to determine a constraint on a possible cosmological variation of the proton-to-electron mass ratio ($\mu =M_{\mathrm{p}}/m_{\mathrm{e}}$) from a comparison with highly redshifted spectral data of quasistellar objects, yielding a fractional change in the mass ratio of $\Delta \mu /\mu =-0.5\pm 3.6\times {10}^{-5}$ ($2\sigma$), which would correspond to a temporal change of $d/dt(\Delta \mu /\mu )=-0.4\pm 3.0\times {10}^{-15}$ per year ($2\sigma$) if a linear cosmological expansion model is assumed.