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 (W_K, z) using a polynomial fit. Based on the reconstructed D_L ^cal (W_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 (W_K = -0.918 ± 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%. Unified Astronomy Thesaurus concepts: Quasars (1319); Cosmological parameters (339); Cosmological models (337); Distance indicators (394); Observational cosmology (1146).