Impact of the 3D source geometry on time-delay measurements of lensed type-Ia supernovae

It has recently been proposed that gravitationally lensed type-Ia supernovae can provide microlensing-free time-delay measurements provided that the measurement is taken during the achromatic expansion phase of the explosion and that color light curves are used rather than single-band light curves. If verified, this would provide both precise and accurate time-delay measurements, making lensed type-Ia supernovae a new golden standard for time-delay cosmography. However, the 3D geometry of the expanding shell can introduce an additional bias that has not yet been fully explored. In this work, we present and discuss the impact of this effect on time-delay cosmography with lensed supernovae and find that on average it leads to a bias of a few tenths of a day for individual lensed systems. This is negligible in view of the cosmological time delays predicted for typical lensed type-Ia supernovae but not for the specific case of the recently discovered type-Ia supernova iPTF16geu, whose time delays are expected to be smaller than a day.