Testing Lens Models of PLCK G165.7+67.0 Using Lensed SN H0pe

Abstract

Supernova H0pe is a multiply-imaged Type Ia supernova (SN~Ia) and the second lensed SN to yield a measurement of the Hubble constant by the time-delay cosmography method, finding $H_0 = 75.4^{+8.1}_{-5.5} \text{km s}^{-1} \text{Mpc}^{-1}$ (Pascale et. al 2025). We investigate the seven lens modeling approaches used to derive $H_0$, assessing their agreement with $\Lambda \text{CDM}$ constraints from SN~Ia surveys through a purely observational comparison. \textbf{We test each lens model by combining its predicted magnifications with the observed time delays to reconstruct the intrinsic SN~Ia luminosity and corresponding distance modulus.} While photometrically derived magnifications yield distance moduli in line with $\Lambda \text{CDM}$ expectations, our comparison reveals that lens model predictions, even the most precise ones, \textbf{consistently overestimate the magnification, with an offset $> 1$~mag}. This known bias, already appreciated by modeling teams, is independently confirmed through our analysis and highlights the value of lensed SNe as a tool to test model accuracy. If unaccounted for, such magnification biases can propagate into uncertainties in derived cosmological parameters, including $H_0$, a critical challenge for precision cosmology using strongly lensed transients.