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Under certain general conditions in an expanding universe, the luminositydistance (d_L) and angular diameter distance (d_A) are connected by theEtherington relation as d_L = d_A (1 + z)^2. The Tolman test suggests the useof 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 neutralhydrogen (HI) masses are seen to be almost linearly correlated with surfacearea, to conduct a new Tolman test. We construct simulated catalogs ofgalaxies, with the observed size-luminosity relation and realistic redshiftevolution of HI mass functions, likely to be detected with the planned SquareKilometer Array (SKA). We demonstrate that these observations may soon providethe best implementation of the Tolman test to detect any violation of theEtherington relation.

A new Tolman test of a cosmic distance duality relation at 21 cm