  The $\textrm{A}^1\Pi-\textrm{X}^1\Sigma^+$ band system of carbon monoxide,
which has been detected in six highly redshifted galaxies ($z=1.6-2.7$), is
identified as a novel probe method to search for possible variations of the
proton-electron mass ratio ($\mu$) on cosmological time scales. Laboratory
wavelengths of the spectral lines of the A-X ($v$,0) bands for $v=0-9$ have
been determined at an accuracy of $\Delta\lambda/\lambda=1.5 \times 10^{-7}$
through VUV Fourier-transform absorption spectroscopy, providing a
comprehensive and accurate zero-redshift data set. For the (0,0) and (1,0)
bands, two-photon Doppler-free laser spectroscopy has been applied at the $3
\times 10^{-8}$ accuracy level, verifying the absorption data. Sensitivity
coefficients $K_{\mu}$ for a varying $\mu$ have been calculated for the CO A-X
bands, so that an operational method results to search for $\mu$-variation.
