How to break the mass sheet degeneracy with the light curves of microlensed Type Ia supernovae

The standardizable nature of gravitationally lensed Type Ia supernovae (glSNe Ia) makes them an attractive target for time-delay cosmography, since a source with known luminosity breaks the mass sheet degeneracy. It is known that microlensing by stars in the lensing galaxy can add significant stochastic uncertainty to the unlensed luminosity, which is often much larger than the intrinsic scatter of the Type Ia population. In this work, we show how the temporal microlensing variations as the supernova (SN) disc expands can be used to improve the standardization of glSNe Ia. We find that SNe are standardizable if they do not cross caustics as they expand. We estimate that this will be the case for ≈6 doubly imaged systems and ≈0.3 quadruply imaged systems per year from the Vera Rubin Observatory (LSST). At the end of the 10 yr LSST survey, these systems should enable us to test for systematics in H₀ due to the mass sheet degeneracy at the 1.00 +0.007 -0.06 per cent level, or 1.8 ± 0.2 per cent if we can only extract time delays from the third of systems with counter-images brighter than i = 24 mag.