  The Wide Field InfraRed Survey Telescope (WFIRST) was the highest ranked
large space-based mission of the 2010 New Worlds, New Horizons decadal survey.
It is now a NASA mission in formulation with a planned launch in the mid-2020s.
A primary mission objective is to precisely constrain the nature of dark energy
through multiple probes, including Type Ia supernovae (SNe Ia). Here, we
present the first realistic simulations of the WFIRST SN survey based on
current hardware specifications and using open-source tools. We simulate SN
light curves and spectra as viewed by the WFIRST wide-field channel (WFC)
imager and integral-field channel (IFC) spectrometer, respectively. We examine
11 survey strategies with different time allocations between the WFC and IFC,
two of which are based upon the strategy described by the WFIRST Science
Definition Team, which measures SN distances exclusively from IFC data. We
propagate statistical and, crucially, systematic uncertainties to predict the
Dark Energy Task Force figure of merit (FoM) for each strategy. Of the
strategies investigated, we find the most successful to be WFC-focused.
However, further work in constraining systematics is required to fully optimize
the use of the IFC. Even without improvements to other cosmological probes, the
WFIRST SN survey has the potential to increase the FoM by more than an order of
magnitude from the current values. Although the survey strategies presented
here have not been fully optimized, these initial investigations are an
important step in the development of the final hardware design and
implementation of the WFIRST mission.
