# Model-independent determination of $H_0$ and $\Omega_{K0}$ from strong lensing and type Ia supernovae

## TL;DR

This paper provides a model-independent measurement of the Hubble constant and spatial curvature using strong lensing and supernova data, confirming the FLRW metric without assuming specific cosmological models.

## Contribution

It introduces a novel, model-independent method to determine $H_0$ and $\,Omega_{K0}$ from strong lensing and supernovae, without relying on assumptions about the Universe's contents or gravity.

## Key findings

- Measured $H_0$ with 6 ext% precision, consistent with other methods.
- Determined spatial curvature $\,Omega_{K0}$ with large uncertainties, compatible with flat universe.
- Confirmed the validity of the FLRW metric through consistency tests.

## Abstract

We present the first determination of the Hubble constant $H_0$ from strong lensing time delay data and type Ia supernova luminosity distances that is independent of the cosmological model. We also determine the spatial curvature model-independently. We assume that light propagation over long distances is described by the FLRW metric and geometrical optics holds, but make no assumption about the contents of the Universe or the theory of gravity on cosmological scales. We find $H_0=75.7^{+4.5}_{-4.4}$ km/s/Mpc and $\Omega_{K0}=0.12^{+0.27}_{-0.25}$. This is a 6\% determination of $H_0$. A weak prior from the cosmic microwave background on the distance to the last scattering surface improves this to $H_0=76.8^{+4.2}_{-3.8}$ km/s/Mpc and $\Omega_{K0}=0.18^{+0.25}_{-0.18}$. Assuming zero spatial curvature, we get $H_0=74.2^{+3.0}_{-2.9}$ km/s/Mpc, a precision of $4\%$. The measurements also provide a consistency test of the FLRW metric: we find no evidence against it.