Measuring Changes in the Fundamental Constants with Redshifted Radio   Absorption Lines
  Strong evidence has recently emerged for a variation in the fine structure constant, $\alpha\equiv e^2/\hbar c$, over the history of the Universe. This was concluded from a detailed study of the relative positions of redshifted optical quasar absorption spectra. However, {\it radio} absorption lines at high redshift offer a much higher sensitivity to a cosmological change in $\alpha$ than optical lines. Furthermore, through the comparison of various radio transitions, \HI, OH and millimetre molecular (e.g. CO) lines, any variations in the proton g-factor, $g_p$, and the ratio of electron/proton masses, $\mu\equiv m_e/m_p$, may also be constrained. Presently, however, systems exhibiting redshifted radio lines are rare with the bias being towards those associated with optically selected QSOs. With its unprecedented sensitivity, large bandwidth and wide field of view, the SKA will prove paramount in surveying the sky for absorbers unbiased by dust extinction. This is expected to yield whole new samples of \HI ~and OH rich systems, the latter of which will prove a useful diagnostic in finding redshifted millimetre absorbers. As well as uncovering many new systems through these blind surveys, the SKA will enable the detection of \HI ~absorption in many more of the present optical sample -- down to column densities of $\sim10^{17}$ \scm, or $\gapp2$ orders of magnitude the sensitivity of the current limits. Armed with these large samples together with the high spectral resolutions, available from the purely radio comparisons, the SKA will provide statistically sound measurements of the values of these fundamental constants in the early Universe, thus providing a physical test of Grand Unified Theories. 
S. J. Curran, N. Kanekar and J. K. Darling