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

We present a new model-independent method to determine spatial curvature and to mitigate the circularity problem affecting the use of quasars as distance indicators. Cosmic-chronometer measurements are used to construct the curvature-dependent luminosity distance $D_L^{cal}({\Omega }_K,z)$ using a polynomial fit. Based on the reconstructed $D_L^{cal}({\Omega }_K,z)$ and the known ultraviolet versus X-ray luminosity correlation of quasars, we simultaneously place limits on the curvature parameter Ω_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 2.1σ 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 ΛCDM model and the R _h = ct universe. Both models account for the data very well, though the optimized flat ΛCDM 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 favored over ΛCDM with a likelihood of ∼57.7% versus 42.3%.