Constraint on a Varying Proton-Electron Mass Ratio 1.5 Billion Years after the Big Bang

A molecular hydrogen absorber at a lookback time of 12.4 billion years, corresponding to 10% of the age of the Universe today, is analyzed to put a constraint on a varying proton-electron mass ratio, $\mu$. A high resolution spectrum of the J1443+2724 quasar, which was observed with the Very Large Telescope, is used to create an accurate model of 89 Lyman and Werner band transitions whose relative frequencies are sensitive to $\mu$, yielding a limit on the relative deviation from the current laboratory value of $\mathrm{\Delta }\mu /\mu =(-9.5\pm {5.4}_{\text{stat}}\pm {5.3}_{\text{syst}})\times {10}^{-6}$.

Figure 1

Part of the final, fitted spectrum of J1443+2724. The sticks indicate the 3 velocity components of each ${\mathrm{H}}_2$ transition. The residuals are shown above the spectrum for the regions fitted. The broad features that surround and overlap the fitted ${\mathrm{H}}_2$ transitions are multiple, unrelated Hi absorption lines arising in other absorbers along the line of sight.

Figure 2

(a) Composite residual spectra of 31 transitions shown for the 3, 4, and 5 VC models. (b) A ${\mathrm{H}}_2$ absorption profile in the J1443+2724 spectrum. The sticks indicate the positions of velocity components for the 3, 4, and 5 VC models.

Figure 3

Statistical $\mathrm{\Delta }\mu /\mu$ constraints obtained from the fiducial 3 VC model, from various tests performed on it, and from the 4 and 5 VC models. The green points refer to fitting low- and high-$J$ transitions with the $z$ and $b$ parameters tied within each group but not between the two groups. The left and the right tests refer to deriving $\mathrm{\Delta }\mu /\mu$ constraints from the two velocity features of ${\mathrm{H}}_2$ separately (see Fig. 2). The orange point was obtained after the spectrum obtained in 2004 has been corrected for long-range wavelength distortions.

Figure 4

The nonrelativistic mass density parameter ${\mathrm{\Omega }}_m$ and the dark energy density parameter ${\mathrm{\Omega }}_{\mathrm{\Lambda }}$ as functions of redshift, with a corresponding lookback time axis on top. Results from various $\mathrm{\Delta }\mu /\mu$ studies: the diamond markers refer to the measurements of rotational transitions of methanol and ammonia [13, 14, 15, 16], while $\mathrm{\Delta }\mu /\mu$ values derived from ${\mathrm{H}}_2$ observations are denoted by circles [18, 19, 20, 21, 23, 24, 38, 39].