The maximum angular-diameter distance in cosmology

Unlike other observational signatures in cosmology, the angular-diameter distance dA (z) uniquely reaches a maximum (at zmax) and then shrinks to zero towards the big bang. The location of this turning point depends sensitively on the model, but has been difficult to measure. In this paper, we estimate and use zmax inferred from quasar cores: (1) by employing a sample of 140 objects yielding a much reduced dispersion due to pre-constrained limits on their spectral index and luminosity, (2) by reconstructing dA (z) using Gaussian processes, and (3) comparing the predictions of seven different cosmologies and showing that the measured value of zmax can effectively discriminate between them. We find that zmax = 1. 70 ± 0. 20 – an important new probe of the Universe’s geometry. The most strongly favoured model is Rh = ct, followed by PlanckΛCDM. Several others, including Milne, Einstein-de Sitter, and Static tired light are strongly rejected. According to these results, the Rh = ct universe, which predicts zmax = 1. 718, has a | 92. 8{\ per\ cent}| probability of being the correct cosmology. For consistency, we also carry out model selection based on dA (z) itself. This test confirms that Rh = ct and PlanckΛCDM are among the few models that account for angular-size data better than those that are disfavoured by zmax. The dA (z) comparison, however, is less discerning than that with zmax, due to the additional free parameter, H0. We find that H0 = 63. 4 ± 1. 2 km s−1 Mpc−1 for Rh = ct, and 69. 9 ± 1. 5 km s−1 Mpc−1 for ΛCDM. Both are consistent with previously measured values in each model, though they differ from each other by over 4σ. In contrast, model selection based on zmax is independent of H0.