# A model-independent determination of the Hubble constant from lensed quasars and supernovae using Gaussian process regression

## TL;DR

This paper presents a model-independent approach using Gaussian process regression to measure the Hubble constant from lensed quasars and supernovae, achieving high precision without assuming a cosmological model.

## Contribution

It introduces a novel Gaussian process-based method to determine H0 directly from lensing and supernova data, avoiding reliance on the ΛCDM model.

## Key findings

- H0 measured as 72.2 ± 2.1 km/s/Mpc assuming flat universe
- H0 measured as 73.0 +2.8/-3.0 km/s/Mpc with curvature prior
- Achieves 2.9% precision in H0 measurement

## Abstract

Strongly lensed quasar systems with time delay measurements provide "time delay distances", which are a combination of three angular diameter distances and serve as powerful tools to determine the Hubble constant $H_0$. However, current results often rely on the assumption of the $\Lambda$CDM model. Here we use a model-independent method based on Gaussian process to directly constrain the value of $H_0$. By using Gaussian process regression, we can generate posterior samples of unanchored supernova distances independent of any cosmological model and anchor them with strong lens systems. The combination of a supernova sample with large statistics but no sensitivity to $H_0$ with a strong lens sample with small statistics but $H_0$ sensitivity gives a precise $H_0$ measurement without the assumption of any cosmological model. We use four well-analyzed lensing systems from the state-of-art lensing program H0LiCOW and the Pantheon supernova compilation in our analysis. Assuming the Universe is flat, we derive the constraint $H_0=72.2 \pm 2.1\,$km/s/Mpc, a precision of $2.9\%$. Allowing for cosmic curvature with a prior of $\Omega_{k}=[-0.2,0.2]$, the constraint becomes $H_0=73.0_{-3.0}^{+2.8}\,$km/s/Mpc.