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.