A Model-independent Method to Determine $H_0$ Using Time-Delay Lensing, Quasars and Type Ia Supernovae

TL;DR

This paper proposes a model-independent method combining supernovae, quasars, and strong lensing time-delay distances to measure the Hubble constant with improved accuracy, especially at higher redshifts.

Contribution

It introduces a novel approach using quasars as a complementary probe to extend redshift coverage and enhance $H_0$ measurement precision without relying on specific cosmological models.

Findings

Quasars can extend the redshift range of distance measurements beyond SNe Ia.

The method improves $H_0$ accuracy from 2.1% to 1.3%.

Model-independent joint constraints are feasible with mock data.

Abstract

Absolute distances from strong lensing can anchor Type Ia Supernovae (SNe Ia) at cosmological distances giving a model-independent inference of the Hubble constant ($H_0$). Future observations could provide strong lensing time-delay distances with source redshifts up to $z\,\simeq\,4$, which are much higher than the maximum redshift of SNe Ia observed so far. In order to make full use of time-delay distances measured at higher redshifts, we use quasars as a complementary cosmic probe to measure cosmological distances at redshifts beyond those of SNe Ia and provide a model-independent method to determine $H_0$. In this work, we demonstrate a model-independent, joint constraint of SNe Ia, quasars, and time-delay distances from strong lensed quasars. We first generate mock data sets of SNe Ia, quasar, and time-delay distances based on a fiducial cosmological model. Then, we calibrate the quasar parameters model independently using Gaussian process (GP) regression with mock SNe Ia data. Finally, we determine the value of $H_0$ model-independently using GP regression from mock quasars and time-delay distances from strong lensing systems. As a comparison, we also show the $H_0$ results obtained from mock SNe Ia in combination with time-delay lensing systems whose redshifts overlap with SNe Ia. Our results show that quasars at higher redshifts show great potential to extend the redshift coverage of SNe Ia and thus enable the full use of strong lens time-delay distance measurements from ongoing cosmic surveys and improve the accuracy of the estimation of $H_0$ from $2.1\%$ to $1.3\%$ when the uncertainties of the time-delay distances are $5\%$ of the distance values.