  Globular clusters are unique tracers of ancient star formation. We determine
the formation efficiencies of globular clusters across cosmic time by modeling
the formation and dynamical evolution of the globular cluster population of a
Milky Way type galaxy in hierarchical cosmology, using the merger tree from the
Via Lactea II simulation. All of the models are constrained to reproduce the
observed specific frequency and initial mass function of globular clusters in
isolated dwarfs. Globular cluster orbits are then computed in a time varying
gravitational potential after they are either accreted from a satellite halo or
formed in situ, within the Milky Way halo. We find that the Galactocentric
distances and metallicity distribution of globular clusters are very sensitive
to the formation efficiencies of globular clusters as a function of redshift
and halo mass. Our most accurate models reveal two distinct peaks in the
globular cluster formation efficiency at z~2 and z~7-12 and prefer a formation
efficiency that is mildly increasing with decreasing halo mass, the opposite of
what expected for feedback-regulated star formation. This model accurately
reproduces the positions, velocities, mass function, metallicity distribution,
and age distribution of globular clusters in the Milky Way and predicts that ~
40% formed in situ, within the Milky Way halo, while the other ~ 60% were
accreted from about 20 satellite dwarf galaxies with Vc > 30 km/s, and about
29% or all globular clusters formed at redshifts z > 7. These results further
strengthen the notion that globular cluster formation was an important mode of
star formation in high-redshift galaxies and likely played a significant role
in the reionization of the intergalactic medium
