A search for varying fundamental constants using hertz-level frequency measurements of cold CH molecules

Many modern theories predict that the fundamental constants depend on time, position or the local density of matter. Here we develop a spectroscopic method for pulsed beams of cold molecules, and use it to measure the frequencies of microwave transitions in CH with accuracy down to 3 Hz. By comparing these frequencies with those measured from sources of CH in the Milky Way, we test the hypothesis that fundamental constants may differ between the high-and low-density environments of the Earth and the interstellar medium. For the fine structure constant we find D alpha/alpha (0.3 +/- 1.1) x 10 (-7), the strongest limit to date on such a variation of alpha. For the electron-to-proton mass ratio we find D mu/mu ( - 0.7 +/- 2.2) x 10 (-7). We suggest how dedicated astrophysical measurements can improve these constraints further and can also constrain temporal variation of the constants.