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 \(D^{\text {Obs}}(z_l) \cdot D_{A,\Delta t}^{\text {Obs}}(z_l, z_s)\), where \(D^{\text {Obs}}(z_l)\) is reconstructed via Gaussian Processes from 99 Einstein radius measurements, and \(D_{A,\Delta t}^{\text {Obs}}(z_l,z_s)\) 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 \(H_0\).