Cosmology with the Wide-Field Infrared Survey Telescope -- Multi-Probe
  Strategies
  We simulate the scientific performance of the Wide-Field Infrared Survey
Telescope (WFIRST) High Latitude Survey (HLS) on dark energy and modified
gravity. The 1.6 year HLS Reference survey is currently envisioned to image
2000 deg$^2$ in multiple bands to a depth of $\sim$26.5 in Y, J, H and to cover
the same area with slit-less spectroscopy beyond z=3. The combination of deep,
multi-band photometry and deep spectroscopy will allow scientists to measure
the growth and geometry of the Universe through a variety of cosmological
probes (e.g., weak lensing, galaxy clusters, galaxy clustering, BAO, Type Ia
supernova) and, equally, it will allow an exquisite control of observational
and astrophysical systematic effects. In this paper we explore multi-probe
strategies that can be implemented given WFIRST's instrument capabilities. We
model cosmological probes individually and jointly and account for correlated
systematics and statistical uncertainties due to the higher order moments of
the density field. We explore different levels of observational systematics for
the WFIRST survey (photo-z and shear calibration) and ultimately run a joint
likelihood analysis in N-dim parameter space. We find that the WFIRST reference
survey alone (no external data sets) can achieve a standard dark energy FoM of
>300 when including all probes. This assumes no information from external data
sets and realistic assumptions for systematics. Our study of the HLS reference
survey should be seen as part of a future community driven effort to simulate
and optimize the science return of WFIRST.
