Cosmology with supernova Encore in the strong lensing cluster MACS J0138-2155: Lens model comparison and H0 measurement

MACS J0138-2155 is the only known cluster to strongly lens two supernovae (SNe), Requiem and Encore, from the same host galaxy at z=1.949. We present seven independent mass models of the galaxy cluster built using six software packages. By conducting a blind analysis (no exchanges of results between modeling teams), we quantified uncertainties due to modeling and software. Through HST, JWST and MUSE observations, we assembled high-quality data products, including eight "gold" lensed image systems consisting of 23 images with secure spectroscopic redshifts, and one "silver" system with a likely redshift value. Restricting to the gold images, we obtain overall consistent model predictions of the positions, magnifications and time delays of SN Encore and SN Requiem images, especially for models with $\chi^2 \leq 25$. We predict the appearance of the next images of SNe Encore and Requiem with a time delay of >~3000 days and of ~3700 to 4000 days, respectively, based on a fiducial cosmological model of $H_0 = 70 {\rm\ km\ s^{-1}\ Mpc^{-1}}$ and $\Omega_{\rm m} = 0.3$. We obtain relations between $H_0$ and the time delays of SNe Encore and Requiem. In particular, for $H_0 = 73 {\rm\ km\ s^{-1}\ Mpc^{-1}}$, the four lowest $\chi^2$ models predict SN Requiem to reappear in ~Apr-Dec 2026; for $H_0 = 67 {\rm\ km\ s^{-1}\ Mpc^{-1}}$, in ~Mar-Nov 2027. Using the newly measured time delay between the two detected images of SN Encore by Pierel et al. (2026) and our mass models, we jointly infer $H_0 = {\rm 66.9^{+11.2}_{-8.1}\ km\ s^{-1}\ Mpc^{-1}}$, where the uncertainty is dominated by that of the time delay. The long delays of the next-appearing SN Requiem and SN Encore images provide excellent opportunities to measure $H_0$ with an uncertainty of 2-3%. Our mass models form the basis for cosmological inference from this unique lens cluster with two strongly lensed SNe. (Abridged)