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We forecast dark energy constraints that could be obtained from a new largesample of Type Ia supernovae where those at high redshift are acquired with theEuclid space mission. We simulate a three-prong SN survey: a z<0.35 nearbysample (8000 SNe), a 0.2<z<0.95 intermediate sample (8800 SNe), and a0.75<z<1.55 high-z sample (1700 SNe). The nearby and intermediate surveys areassumed to be conducted from the ground, while the high-z is a joint ground-and space-based survey. This latter survey, the "Dark Energy SupernovaInfra-Red Experiment" (DESIRE), is designed to fit within 6 months of Euclidobserving time, with a dedicated observing program. We simulate the SN eventsas they would be observed in rolling-search mode by the various instruments,and derive the quality of expected cosmological constraints. We account forknown systematic uncertainties, in particular calibration uncertaintiesincluding their contribution through the training of the supernova model usedto fit the supernovae light curves. Using conservative assumptions and a 1-Dgeometric Planck prior, we find that the ensemble of surveys would yieldcompetitive constraints: a constant equation of state parameter can beconstrained to sigma(w)=0.022, and a Dark Energy Task Force figure of merit of203 is found for a two-parameter equation of state. Our simulations thusindicate that Euclid can bring a significant contribution to a purelygeometrical cosmology constraint by extending a high-quality SN Hubble diagramto z~1.5. We also present other science topics enabled by the DESIRE Euclidobservations

Extending the supernova Hubble diagram to z~1.5 with the Euclid space mission