Cosmological tests using the angular size of galaxy clusters

We use measurements of the galaxy-cluster angular size versus redshift to test and compare the standard model (ΔCDM) and the R_h = ct Universe. We show that the latter fits the data with a reduced χ² _dof = 0.786 for a Hubble constant H₀ = 72.6^+3.8 _-3.4 km s^-1 Mpc^-1, and H₀ is the sole parameter in this model. By comparison, the optimal flat cold dark matter (ΔCDM) model, with two free parameters (including ω_m = 0.50 and H₀ = 73.9^+10.6 _-9.5 km s^-1Mpc^-1), fits the angular-size data with a reduced x² _dof = 0.806. On the basis of their x² _dof values alone, both models appear to account for the data very well in spite of the fact that the R_h = ct Universe expands at a constant rate, while ΔCDM does not. However, because of the different number of free parameters in these models, selection tools, such as the Bayes Information Criterion, favour R_h = ct over CDM with a likelihood of ~86 per cent versus ~14 per cent. These results impact the question of galaxy growth at large redshifts. Previous work suggested an inconsistency with the underlying cosmological model unless elliptical and disc galaxies grew in size by a surprisingly large factor ~6 from z ~ 3 to 0. The fact that both CDM and R_h = ct fit the cluster-size measurements quite well casts some doubt on the suggestion that the unexpected result with individual galaxies may be due to the use of an incorrect expansion scenario, rather than astrophysical causes, such as mergers and/or selection effects.