Cosmology-independent Estimate of the Hubble Constant and Spatial Curvature Using Time-delay Lenses and Quasars

TL;DR

This paper introduces a model-independent method using quasars and strong lensing to estimate the Hubble constant and spatial curvature, extending redshift coverage and improving precision over previous techniques.

Contribution

It proposes a novel approach combining quasars with time-delay lensing data to simultaneously constrain $H_0$ and $\,Omega_K$ in a model-independent way.

Findings

Estimated $H_0$ around 75 km/s/Mpc, consistent with local measurements.

Found spatial curvature $\,Omega_K$ consistent with zero, supporting a flat universe.

Achieved 2.5 ext{%} precision on $H_0$ when assuming flatness.

Abstract

With the distance sum rule in the Friedmann-Lema\^{\i}tre-Robertson-Walker metric, model-independent constraints on both the Hubble constant $H_0$ and spatial curvature $\Omega_{K}$ can be obtained using strong lensing time-delay data and Type Ia supernova (SN Ia) luminosity distances. This method is limited by the relative low redshifts of SNe Ia, however. Here, we propose using quasars as distance indicators, extending the coverage to encompass the redshift range of strong lensing systems. We provide a novel and improved method of determining $H_0$ and $\Omega_{K}$ simultaneously. By applying this technique to the time-delay measurements of seven strong lensing systems and the known ultraviolet versus X-ray luminosity correlation of quasars, we constrain the possible values of both $H_0$ and $\Omega_{K}$, and find that $H_0=75.3^{+3.0}_{-2.9}$ km $\rm s^{-1}$ $\rm Mpc^{-1}$ and $\Omega_{K}=-0.01^{+0.18}_{-0.17}$. The measured $\Omega_{K}$ is consistent with zero spatial curvature, indicating that there is no significant deviation from a flat universe. If we use flatness as a prior, we infer that $H_0=75.3^{+1.9}_{-1.9}$ km $\rm s^{-1}$ $\rm Mpc^{-1}$, representing a precision of 2.5\%. If we further combine these data with the 1048 current Pantheon SNe Ia, our model-independent constraints can be further improved to $H_0=75.3^{+3.0}_{-2.9}$ km $\rm s^{-1}$ $\rm Mpc^{-1}$ and $\Omega_{K}=0.05^{+0.16}_{-0.14}$. In every case, we find that the Hubble constant measured with this technique is strongly consistent with the value ($\sim 74$ km $\rm s^{-1}$ $\rm Mpc^{-1}$) measured using the local distance ladder, as opposed to the value optimized by {\it Planck}.