Cosmological Constraints on a Temporal Variation of the Proton-to-electron Mass Ratio based on the Red-shifted Lines of Extragalactic Argonium

Abstract

The sensitivity coefficients of the argonium ground ${{X}^{1}}{{\Sigma }^{ + }}$-state rotational lines with respect to the reduced molecular mass $\mu$ are evaluated using the Dunham’s molecular constants accounting for Born–Oppenheimer approximation breakdown. They are used to constrain presumable temporal variation in the proton-to-electron mass ratio $\gamma = {{m}_{p}}{\text{/}}{{m}_{e}}$ on cosmological time scales by a comparison of absorption lines of extragalactic argonium with their recently measured laboratory counterparts. The $J = 0 \to 1$ transition frequencies of the most cosmically abundant ³⁶ArH⁺ and ³⁸ArH⁺ isotopomers are derived from available ALMA observations of an unnamed foreground galaxy at $z \approx 0.89$ in the direction of the radio-loud quasar PKS 1830-211. The upper limit of the possible variation $\Delta \gamma {\text{/}}\gamma$ over the timescale of about 7 Gyr is conservatively estimated to be $< {\kern 1pt} {{10}^{{ - 5}}}$. Its value is limited by accuracy both of observed transition frequencies and of the adopted redshift $z$.