The design reference mission described in detail in the Final Report of the WFIRST-AFTA Science Definition Team has the following three key science components. This science program will be addressed using two instruments and five observing surveys/programs.
WFIRST will measure the equation of state of dark energy and its time evolution, helping determine whether it is a cosmological constant, through all of the major methods suggested thus far. Its wide-area, multicolor imaging survey, covering over 2,000 square degrees, will enable weak lensing shape and photometric redshift measurements of hundreds of millions of galaxies, which will in turn yield precise measurements of distances and matter clustering through measurements of cosmic shear, galaxy-galaxy lensing, and the abundance and mass profiles of galaxy clusters. Its wide-area spectroscopic survey, over the same area, will determine million of redshifts for galaxies between z=1 and 3, thus measuring the evolution of the size of the Universe and constraining the scale of Baryon Acoustic Oscillations to 0.3%, as well as measuring the growth of structure via redshift-space distortions. The tiered supernova surveys, covering 5 to 27 square degrees, will discover and measure precise distances to thousands of Type Ia supernovae up to redshift z=2.
WFIRST will use time-series microlensing imaging observations of Milky Way Bulge stars to determine the distribution of exoplanets down to sub-Earth masses in a wide range of orbital radii, including the habitable zone, the outer regions of planetary systems, and free-floating planets. An area of over 2 square degrees will be observed with 15 minute cadence over 72 consecutive days in each of six campaigns, resulting in the likely discovery of over 2000 bound exoplanets, including about 400 of Earth mass and below.
The coronagraphic instrument on WFIRST will be capable of directly imaging planets similar to those in our Solar System, measuring for the first time the photometric properties of the 'mini-Neptune' or 'super-Earth' planets - objects that Kepler has shown to be the most common planets in our galaxy, but with no analog in our own solar system. It will also provide crucial technology development for possible future missions aimed at detecting signs of life in the atmospheres of Earth-like exoplanets.
With a field of view 100 times larger than that of HST and JWST instruments, the Wide Field Imager will provide the largest-scale high-resolution images of the Universe that astronomers have ever had. The data collected for the planned WFIRST surveys will form a treasure trove for archival Guest Investigator studies in many areas of General Astrophysics. Examples of science projects enabled by the data in the High-Latitude Survey include: mapping the formation of cosmic structure in the first billion years after the Big Bang via the detection and characterization of over 10,000 galaxies at z > 8; finding over 2,000 QSOs at z > 7; quantifying the distribution of dark matter on intermediate and large scales through lensing in clusters and in the field; identifying the most extreme star-forming galaxies and shock-dominated systems at 1 < z < 2; carrying out a complete census of star-forming galaxies and the faint end of the QSO luminosity function at z ~ 2, including their contribution to the ionizing radiation; and determining the kinematics of stellar streams in the Local Group through proper motions.
In addition, 25% of the mission time will be set aside for Guest Observer programs. This will allow use of the broad range of WFIRST instruments capabilities, namely wide-field imaging and slitless spectroscopy, integral-field spectroscopy, and coronographic imaging and spectroscopy, for many additional studies in General Astrophysics. Some examples include: studying young clusters and embedded star forming regions within the Galaxy; reaching the very faint end of the stellar luminosity function via very deep observations of Local-Group galaxies; mapping the core of the Virgo cluster; coronographic observations of AGNs to investigate their stellar populations in comparison to normal galaxies; and follow-up studies of systems found through HLS observations (high-redshift QSOs and galaxies, galaxy clusters).
Appendix D of the Final Report of the WFIRST-AFTA Science Definition Team includes one-page summaries of many other possible Guest Investigator and Guest Observer Programs, covering areas of science ranging from the Solar System to Cosmology.