Dimensionless constants and cosmological measurements
  The laws of physics have a set of fundamental constants, and it is generally
admitted that only dimensionless combinations of constants have physical
significance. These combinations include the electromagnetic and gravitational
fine structure constants, $\alpha=e^2/4\pi\epsilon_0\hbar c$ and
$\alpha_G=Gm_p^2/\hbar c$, along with the ratios of elementary-particles
masses. Cosmological measurements clearly depend on the values of these
constants in the past and can therefore give information on their time
dependence if the effects of time-varying constants can be separated from the
effects of cosmological parameters. The latter can be eliminated by using pairs
of redundant measurements and here we show how such pairs conspire to give
information only on dimensionless combinations of constants. Among other
possibilities, we will use distance measurements based on Baryon Acoustic
Oscillations (BAO) and on type Ia supernova. The fact that measurements yield
information only on dimensionless combinations is traced to the fact that
distances between co-moving points expand following the same function of time
that governs the redshift of photon wavelengths.
