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

Abstract

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 using a polynomial fit. Based on the reconstructed 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 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 ?CDM model and the R-h = ct universe. Both models account for the data very well, though the optimized flat ?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 favored over ?CDM with a likelihood of similar to 57.7% versus 42.3%.