Model-independent Distance Calibration and Curvature Measurement using Quasars and Cosmic Chronometers

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 $D^{\rm cal}_{L}(\Omega_{K},z)$ using a polynomial fit. Based on the reconstructed $D^{\rm cal}_{L}(\Omega_{K},z)$ 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 ($\Omega_{K}=-0.918\pm0.429$) 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 $R_{\rm h}=ct$ universe. Both models account for the data very well, though the optimized flat $\Lambda$CDM model has one more free parameter than $R_{\rm h}=ct$, and is penalized more heavily by the Bayes Information Criterion. We find that $R_{\rm h}=ct$ is slightly favoured over $\Lambda$CDM with a likelihood of $\sim57.7\%$ versus 42.3\%.