We present a new model-independent method to determine the spatial curvature and to mitigate the circularity problem affecting the use of quasars as distance indicators .
The cosmic-chronometer measurements are used to construct the curvature-dependent luminosity distance D ^ { cal } _ { L } ( \Omega _ { K } ,z ) using a polynomial fit .
Based on the reconstructed D ^ { cal } _ { L } ( \Omega _ { K } ,z ) and the known ultraviolet versus X-ray luminosity correlation of quasars , we simultaneously place limits on the curvature parameter \Omega _ { K } and the parameters characterizing the luminosity correlation function .
This model-independent analysis suggests that a mildly closed Universe ( \Omega _ { K } = -0.918 \pm 0.429 ) is preferred at the 2.1 \sigma level .
With the calibrated luminosity correlation , we build a new data set consisting of 1598 quasar distance moduli , and use these calibrated measurements to test and compare the standard \Lambda CDM model and the R _ { h } = ct universe .
Both models account for the data very well , though the optimized flat \Lambda CDM model has one more free parameter than R _ { h } = ct , and is penalized more heavily by the Bayes Information Criterion .
We find that R _ { h } = ct is slightly favoured over \Lambda CDM with a likelihood of \sim 57.7 \% versus 42.3 % .