Comparison of cosmological models using Bayesian theory

Using the Bayesian theory of model comparison, a new cosmological model due to John and Joseph [M. V. John and K. Babu Joseph, Phys. Rev. D 61, 087304 (2000)] is compared with the standard ${\Omega }_{\Lambda }\ne 0$ cosmological model. Their analysis based on the recent apparent magnitude-redshift data of type Ia supernovas found evidence against the new model; our more careful analysis finds instead that this evidence is not strong. On the other hand, we find that the angular size-redshift data from compact (milliarcsecond) radio sources do not discriminate between the two models. Our analysis serves as an example of how to compare the relative merits of cosmological models in general, using the Bayesian approach.