First Cosmological Constraints on the Proton-to-electron Mass Ratio from Observations of Rotational Transitions of Methanol

We have used the Australia Telescope Compact Array to measure the absorption from the 2₀ → 3_-1 E 12.2 GHz transition of methanol toward the z = 0.89 lensing galaxy in the PKS B1830-211 gravitational lens system. Comparison of the velocity of the main absorption feature with the published absorption spectrum from the 1₀ → 2_-1 E transition of methanol shows that they differ by -0.6 ± 1.6 km s^-1. We can use these observations to constrain the changes in the proton-to-electron mass ratio μ from z = 0.89 to the present to 0.8 ± 2.1 × 10^-7. This result is consistent, and of similar precision to recent observations at z = 0.68 achieved through comparison of a variety of rotational and inversion transitions, and approximately a factor of two better than previous constraints obtained in this source. Future more sensitive observations that incorporate additional rotational methanol transitions offer the prospect of improving current results by a factor of 5-10.