A Joint Analysis of Strong Lensing and Type Ia Supernovae to Determine the Hubble Constant

We present a cosmological model-independent determination of the Hubble constant, $H_0$, by combining time-delay measurements from seven TDCOSMO systems, Einstein radius measurements, and Type Ia Supernovae data sourced from the Pantheon+ sample. For each lens of time-delay system, we calculate the angular diameter distance $D_{A_l}$ using the product $D^{\text{Obs}}(z_l)\cdot D_{A,\mathrm{\Delta }t}^{\text{Obs}}(z_l,z_s)$, where $D^{\text{Obs}}(z_l)$ is reconstructed via Gaussian Processes from 99 Einstein radius measurements, and $D_{A,\mathrm{\Delta }t}^{\text{Obs}}(z_l,z_s)$ is the time-delay angular distance. We also reconstruct the unanchored luminosity distance $H_0{D}_L(z_l)$ from supernova data. By using the cosmic distance duality relation validity, we anchor $D_{A_l}$ and $H_0{D}_L(z_l)$ to infer $H_0=70.55\pm 7.44$ km/s/Mpc (68% CL). Our result, though not resolving the Hubble tension, offers a cosmological model-independent consistency check and highlights the potential of using strong lensing and supernovae data via the cosmic distance duality relation to constrain $H_0$.