The $z \sim 2$ $\rm{[O\ III]}$ Luminosity Function of Grism-selected
  Emission-line Galaxies
  Upcoming missions such as Euclid and the Nancy Grace Roman Space Telescope
(Roman) will use emission-line selected galaxies to address a variety of
questions in cosmology and galaxy evolution in the $z>1$ universe. The optimal
observing strategy for these programs relies upon knowing the number of
galaxies that will be found and the bias of the galaxy population. Here we
measure the $\rm{[O\ III]}\ \lambda 5007$ luminosity function for a vetted
sample of 1951 $m_{\rm J+JH+H} < 26$ galaxies with unambiguous redshifts
between $1.90 < z < 2.35$, which were selected using HST/WFC3 G141 grism frames
made available by the 3D-HST program. These systems are directly analogous to
the galaxies that will be identified by the Euclid and Roman missions, which
will utilize grism spectroscopy to find $\rm{[O\ III]}\ \lambda 5007$-emitting
galaxies at $0.8 \lesssim z \lesssim 2.7$ and $1.7 \lesssim z \lesssim 2.8$,
respectively. We interpret our results in the context of the expected number
counts for these upcoming missions. Finally, we combine our dust-corrected
$\rm{[O\ III]}$ luminosities with rest-frame ultraviolet star formation rates
to present a new calibration of the SFR density associated with $1.90 < z <
2.35$ $\rm{[O\ III]}$-emitting galaxies. We find that these grism-selected
galaxies contain roughly half of the total star formation activity at $z\sim2$.
