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

TL;DR

This paper introduces a model-independent method to measure cosmic curvature using quasars and cosmic chronometers, suggesting a mildly closed universe and comparing standard cosmological models with new calibrated quasar data.

Contribution

The study develops a novel approach to determine spatial curvature without relying on specific cosmological models, using quasars and cosmic chronometers to calibrate luminosity correlations.

Findings

Mildly closed universe preferred at 2.1σ level

Calibrated 1598 quasar distance moduli dataset created

R_h=ct universe slightly favored over ΛCDM

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 $D^{\rm cal}_{L}(\Omega_{K},z)$ 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. 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 $R_{\rm h}=ct$ universe. Both models account for the data very well, though the optimized flat $\Lambda$CDM model has one more free parameter than $R_{\rm h}=ct$, and is penalized more heavily by the Bayes Information Criterion. We find that $R_{\rm h}=ct$ is slightly favoured over $\Lambda$CDM with a likelihood of $\sim57.7\%$ versus 42.3\%.