The angular size-redshift relation in power-law cosmologies

A linear evolution of the cosmological scale factor is a feature in several models designed to solve the cosmological constant problem via a coupling between scalar or tensor classical fields to the spacetime curvature as well as in some alternative gravity theories. In this paper, by assuming a general time dependence of the scale factor, R ~ t(alpha), we investigate observational constraints on the dimensionless parameter (alpha) from measurements of the angular size for a large sample of milliarcsecond compact radio sources. In particular, we find that a strictly linear evolution, i.e., (alpha) =~1, is favoured by these data, which is also in agreement with limits obtained from other independent cosmological tests. The dependence of the critical redshift zm (at which a given angular size takes its minimal value) on the index (alpha) is briefly discussed.