Model selection based on the angular-diameter distance to the compact structure in radio quasars

Of all the distance and temporal measures in cosmology, the angular-diameter distance, dA(z), uniquely reaches a maximum value at some finite redshift $z_{\rm max}$ and then decreases to zero towards the Big Bang. This effect has been difficult to observe due to a lack of reliable, standard rulers, though refinements to the identification of the compact structure in radio quasars may have overcome this deficiency. In this letter, we assemble a catalog of 140 such sources with $0\lesssim z\lesssim 3$ for model selection and the measurement of $z_{\rm max}$ . In flat ΛCDM, we find that $\Omega_{\rm m}= 0.24^{+0.1}_{-0.09}$ , fully consistent with the Planck optimized value, with $z_{\rm max}=1.69$ . Both of these values are associated with a dA(z) indistinguishable from that predicted by the zero active mass condition, $\rho+3p=0$ , in terms of the total pressure p and total energy density ρ of the cosmic fluid. An expansion driven by this constraint, known as the $R_{\rm h}=ct$ universe, has $z_{\rm max}=1.718$ , which differs from the ΛCDM optimized value by less than $\sim 1.6\%$ . Indeed, the Bayes Information Criterion favours $R_{\rm h}=ct$ over flat ΛCDM with a likelihood of $\sim 81\%$ vs. $19\%$ , suggesting that the optimized parameters in Planck ΛCDM mimic the constraint $p=-\rho/3$