  Double neutron stars (DNSs) have been observed as Galactic radio pulsars, and
the recent discovery of gravitational waves from the DNS merger GW170817 adds
to the known DNS population. We perform rapid population synthesis of massive
binary stars and discuss model predictions, including formation rates, mass
distributions, and delay time distributions. We vary assumptions and parameters
of physical processes such as mass transfer stability criteria, supernova kick
distributions, remnant mass distributions and common-envelope energetics. We
compute the likelihood of observing the orbital period-eccentricity
distribution of the Galactic DNS population under each of our population
synthesis models, allowing us to quantitatively compare the models. We find
that mass transfer from a stripped post-helium-burning secondary (case BB) onto
a neutron star is most likely dynamically stable. We also find that a natal
kick distribution composed of both low (Maxwellian $\sigma=30\rm~km~s^{-1}$)
and high ($\sigma=265\rm~km~s^{-1}$) components is preferred over a single
high-kick component. We find that the observed DNS mass distribution can place
strong constraints on model assumptions.
