  Infrared magnitude-redshift relations for the 3CR and 6C samples of radio
galaxies are presented for a wide range of plausible cosmological models,
including those with non-zero cosmological constant OmegaLambda. Variations in
the galaxy formation redshift, metallicity and star formation history are also
considered. The results of the modelling are displayed in terms of magnitude
differences between the models and no-evolution tracks, illustrating the amount
of K-band evolution necessary to account for the observational data. Given a
number of plausible assumptions, the results of these analyses suggest that:
(i) cosmologies which predict T_0xH_0>1 (where T_0 denotes the current age of
the universe) can be excluded; (ii) the star formation redshift should lie in
the redshift interval 5<z<20, values towards the lower end of the range being
preferred in cosmologies with larger values of T_0xH_0; (iii) the Einstein-de
Sitter model provides a reasonable fit to the data; (iv) models with finite
values of OmegaLambda can provide good agreement with the observations only if
appropriate adjustments of other parameters such as the galaxy metallicities
and star-formation histories are made. Without such modifications, even after
accounting for stellar evolution, the high redshift radio galaxies are more
luminous (ie. more massive) than those nearby in models with finite
OmegaLambda, including the favoured model with Omega=0.3, OmegaLambda=0.7. For
cosmological models with larger values of T_0xH_0, the conclusions are the same
regardless of whether any adjustments are made or not. The implications of
these results for cosmology and models of galaxy formation are discussed.
