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

Abstract

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 $D_L^{\mathrm{cal}}({\Omega }_K,z)$ using a polynomial fit. Based on the reconstructed $D_L^{\mathrm{cal}}({\Omega }_K,z)$ 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 $R_{\mathrm{h}}=ct$ universe. Both models account for the data very well, though the optimized flat $\Lambda$CDM model has one more free parameter than $R_{\mathrm{h}}=ct$, and is penalized more heavily by the Bayes Information Criterion. We find that $R_{\mathrm{h}}=ct$ is slightly favoured over $\Lambda$CDM with a likelihood of $\sim 57.7\%$ versus 42.3\%.

8 pages, 5 figures, 2 tables. Accepted for publication in ApJ

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