A Hubble Constant Determination Through Quasar Time Delays and Type Ia Supernovae

Abstract: This paper presents a new model-independent constraint on the Hubble constant ($H_0$) by anchoring relative distances from Type Ia supernovae (SNe Ia) observations to absolute distance measurements from time-delay strong Gravitational Lensing (SGL) systems. The approach only uses the validity of the cosmic distance duality relation (CDDR) to derive constraints on $H_0$. By using Gaussian Process (GP) regression to reconstruct the unanchored luminosity distance from the Pantheon$+$ compilation to match the time-delay angular diameter distance at the redshift of the lenses, one yields a value of $H_0 = 75.57 \pm 4.415$ km/s/Mpc at a 68\% confidence level. The result aligns well with the local estimate from Cepheid variables within the $1\sigma$ confidence region, indicating consistency with late-universe probes.