  We use measurements of the galaxy-cluster angular size versus redshift to
test and compare the standard model (LCDM) and the R_h=ct Universe. We show
that the latter fits the data with a reduced chi^2_dof=0.786 for a Hubble
constant H_0= 72.6 (-3.4+3.8) km/s/Mpc, and H_0 is the sole parameter in this
model. By comparison, the optimal flat LCDM model, with two free parameters
(including Omega_m=0.50 and H_0=73.9 (-9.5+10.6) km/s/Mpc), fits the
angular-size data with a reduced chi^2_dof=0.806. On the basis of their
chi^2_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
LCDM 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 LCDM with a likelihood of ~86% versus ~14%. These results impact
the question of galaxy growth at large redshifts. Previous work suggested an
inconsistency with the underlying cosmological model unless elliptical and disk
galaxies grew in size by a surprisingly large factor ~6 from z~3 to 0. The fact
that both LCDM 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.
