  Gamma-ray observations have shown pulsars to be efficient converters of
rotational energy into GeV photons and it is of wide-ranging interest to
determine their contribution to the gamma-ray background. We arrive at flux
predictions from both the young (<~ Myr) and millisecond (~Gyr) Galactic pulsar
populations. We find that unresolved pulsars can yield both a significant
fraction of the excess GeV gamma rays near the Galactic Center and an inverse
Compton flux in the inner kpc similar to that inferred by Fermi. We compare
models of the young pulsar population and millisecond pulsar population to
constraints from gamma-ray and radio observations. Overall, we find that the
young pulsars should outnumber millisecond pulsars as unassociated gamma-ray
point sources in this region. The number of young radio pulsars discovered near
the Galactic Center is in agreement with our model of the young pulsar
population. Deeper radio observations at higher latitudes can constrain the
total gamma-ray emission from both young and millisecond pulsars from the inner
galaxy. While this is a step towards better understanding of pulsars, cosmic
rays in the Milky Way, and searches for dark matter, we also discuss a few
interesting puzzles that arise from the underlying physics of pulsar emission
and evolution.
