Infrared magnitude-redshift relations ( K-z 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 \Omega _ { \Lambda } .
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 _ { 0 } } \times { H _ { 0 } } \mathrel { \hbox to 0.0 pt { \lower 3.0 pt \hbox { $ \mathchar 536 $ } % \hss } \raise 2.0 pt \hbox { $ \mathchar 318 $ } } 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 \leq z _ { f } \leq 20 , values towards the lower end of the range being preferred in cosmologies with larger values of { T _ { 0 } } \times { H _ { 0 } } ; ( iii ) the Einstein-de Sitter model ( \Omega _ { 0 } = 1 , \Omega _ { \Lambda } = 0 ) provides a reasonable fit to the data ; ( iv ) models with finite values of \Omega _ { \Lambda } 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 ( that is , more massive ) than those nearby in models with finite \Omega _ { \Lambda } , including the favoured model with \Omega _ { 0 } = 0.3 , \Omega _ { \Lambda } = 0.7 .
For cosmological models with larger values of { T _ { 0 } } \times { H _ { 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 .