Since the realization in the 1950s that the majority of catalogued radio sources are extragalactic and that some of the strongest are at cosmological distances, the application of radio observations to cosmological studies has been a central theme in radio astronomy.
The ratios of flux density to luminosity and angular size to projected linear size at different redshifts can, in principle, distinguish between world models by their geometrical properties and measure directly such basic parameters as the Hubble constant H0 and the deceleration parameter q0. The sensitivity and resolution of modern radio telescopes are more than adequate to make such measurements on a variety of sources, even at redshifts z >> 1. Unfortunately, no "standard candle" or "standard rod" sources with luminosities or linear sizes known in a model-independent way have yet been recognized. Not only do the luminosities and sizes of extragalactic radio sources cover a wide range, but also their median values in radio-source populations evolve with cosmological epoch.
A less direct, but so far more successful, approach is to obtain complete samples of radio sources and model statistics describing radio-source populations. For example, the flux-density distribution of sources led to the discovery of evolution on cosmological time scales and the rejection of the steady-state world model. Such cosmological studies of radio-source populations might be used to constrain astrophysical theories of radio sources, their parent galaxies, their environments, and their evolution. Radio-selected samples are particularly well suited to these cosmological investigations for several reasons. Modern radio surveys are statistically complete and quite reliable, and radio flux densities are routinely measured with high accuracy. Radio samples are not badly confused by galactic stars, and they are not affected by dust obscuration in our galaxy, intervening material at high redshifts, or the host galaxies of the sources themselves (Ostriker and Heisler 1984). Radio sources have fairly smooth power law spectra, so there is no sharp redshift cutoff or discrimination against sources in certain redshift bands. Finally, many radio sources that have been found at redshifts z 1 are so luminous that they could easily be detected in moderately sensitive surveys even at very high redshifts (z 10). The biggest limitation of radio-selected samples is their dependence on optical identifications and spectroscopy for information about distance and host-galaxy morphology (elliptical galaxy, spiral galaxy, quasar, etc.). Only for the N 200 strongest radio sources are the optical identifications and spectroscopy complete. The redshift distributions of most faint sources can only be estimated with the aid of evolutionary models constrained by statistical data - source counts, angular-size distributions, etc. This chapter describes some of the tests of world models and cosmological evolution that can be made using discrete radio sources.