A new Tolman test of a cosmic distance duality relation at 21 cm
  Under certain general conditions in an expanding universe, the luminosity
distance (d_L) and angular diameter distance (d_A) are connected by the
Etherington relation as d_L = d_A (1 + z)^2. The Tolman test suggests the use
of objects of known surface brightness, to test this relation. In this letter,
we propose the use of redshifted 21 cm signal from disk galaxies, where neutral
hydrogen (HI) masses are seen to be almost linearly correlated with surface
area, to conduct a new Tolman test. We construct simulated catalogs of
galaxies, with the observed size-luminosity relation and realistic redshift
evolution of HI mass functions, likely to be detected with the planned Square
Kilometer Array (SKA). We demonstrate that these observations may soon provide
the best implementation of the Tolman test to detect any violation of the
Etherington relation.
