Recently, a stringent constraint on the change in the proton-to-electron mass ratio at a redshift of 0.89 has been established using theoretical predictions and radio observations of the methanol molecule. To get an insight at deeper look-back times, accurate determinations of variations of the proton-to-electron mass ratio at higher redshifts are needed.
We propose a microwave probe of the proton-to-electron mass ratio employing the primordial molecular ions H-2(+), D-2(+), and He-2(+) considering redshifts from 0 to 70. Microwave rovibronic transitions of these ions, which are presented here, crucially exhibit high or very high sensitivities to a variation of the proton-to-electron mass ratio and could in principle be detected by the Atacama Large Millimeter/submillimiter Array.