Unlike other observational signatures in cosmology , the angular-diameter distance d _ { A } ( z ) uniquely reaches a maximum ( at z _ { max } ) 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 z _ { max } 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 d _ { A } ( z ) using Gaussian processes , and ( 3 ) comparing the predictions of seven different cosmologies and showing that the measured value of z _ { max } can effectively discriminate between them .
We find that z _ { max } = 1.70 \pm 0.20 —an important new probe of the Universe ’ s geometry .
The most strongly favoured model is R _ { h } = ct , followed by Planck \Lambda CDM .
Several others , including Milne , Einstein-de Sitter and Static tired light are strongly rejected .
According to these results , the R _ { h } = ct universe , which predicts z _ { max } = 1.718 , has a \sim 92.8 \% probability of being the correct cosmology .
For consistency , we also carry out model selection based on d _ { A } ( z ) itself .
This test confirms that R _ { h } = ct and Planck \Lambda CDM are among the few models that account for angular-size data better than those that are disfavoured by z _ { max } .
The d _ { A } ( z ) comparison , however , is less discerning than that with z _ { max } , due to the additional free parameter , H _ { 0 } .
We find that H _ { 0 } = 63.4 \pm 1.2 km s ^ { -1 } Mpc ^ { -1 } for R _ { h } = ct , and 69.9 \pm 1.5 km s ^ { -1 } Mpc ^ { -1 } for \Lambda CDM .
Both are consistent with previously measured values in each model , though they differ from each other by over 4 \sigma .
In contrast , model selection based on z _ { max } is independent of H _ { 0 } .