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Molecular transitions recently discovered at redshift   z  abs = 2.059  towards the bright background quasar  J2123−0050  are analysed to limit cosmological variation in the proton‐to‐electron mass ratio,  μ≡ m  p / m  e  . Observed with the Keck telescope, the optical echelle spectrum has the highest resolving power and largest number (86) of H 2  transitions in such analyses so far. Also, (seven) HD transitions are used for the first time to constrain μ‐variation. These factors, and an analysis employing the fewest possible free parameters, strongly constrain μ's relative deviation from the current laboratory value:  Δμ/μ= (+5.6 ± 5.5 stat ± 2.9 sys ) × 10 −6  , indicating an insignificantly larger μ in the absorber. This is the first Keck result to complement recent null constraints from three systems at   z  abs  &gt; 2.5  observed with the Very Large Telescope. The main possible systematic errors stem from wavelength calibration uncertainties. In particular, distortions in the wavelength solution on echelle order scales are estimated to contribute approximately half the total systematic error component, but our estimate is model dependent and may therefore under or overestimate the real effect, if present.  To assist future μ‐variation analyses of this kind, and other astrophysical studies of H 2  in general, we provide a compilation of the most precise laboratory wavelengths and calculated parameters important for absorption‐line work with H 2  transitions redwards of the hydrogen Lyman limit.

Keck telescope constraint on cosmological variation of the proton‐to‐electron mass ratio