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The $Euclid$ mission will provide first-of-its-kind coverage in thenear-infrared over deep (three fields, $\sim$10-20 square degrees each) andwide ($\sim$10000 square degrees) fields. While the survey is not designed todiscover transients, the deep fields will have repeated observations over atwo-week span, followed by a gap of roughly six months. In this analysis, weexplore how useful the deep field observations will be for measuring propertiesof Type Ia supernovae (SNe Ia). Using simulations that include $Euclid$'splanned depth, area and cadence in the deep fields, we calculate that more than3700 SNe between $0.0<z<1.5$ will have at least five $Euclid$ detections aroundpeak with signal-to-noise ratio larger than 3. While on their own, $Euclid$light curves are not good enough to directly constrain distances, when combinedwith LSST deep field observations, we find that uncertainties on SN distancesare reduced by 20-30% for $z<0.8$ and by 40-50% for $z>0.8$. Furthermore, wepredict how well additional $Euclid$ mock data can be used to constrain a keysystematic in SN Ia studies - the size of the luminosity 'step' found betweenSNe hosted in high mass ($>10^{10} M_{\odot}$) and low mass ($>10^{10}M_{\odot}$) galaxies. This measurement has unique information in the rest-frameNIR. We predict that if the step is caused by dust, we will be able to measureits reduction in the NIR compared to optical at the 4$\sigma$ level. Wehighlight that the LSST and $Euclid$ observing strategies used in this work arestill provisional and some level of joint processing is required. Still, thesefirst results are promising, and assuming $Euclid$ begins observations wellbefore the Nancy Roman Space Telescope (Roman), we expect this dataset to beextremely helpful for preparation for Roman itself.

Type Ia Supernova cosmology combining data from the $Euclid$ mission and the Vera C. Rubin Observatory