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

Understand

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.