  We investigate star formation at very early evolutionary phases in five
massive clouds in the inner 500 pc of the Galaxy, the Central Molecular Zone.
Using interferometer observations of H$_2$O masers and ultra-compact H II
regions, we find evidence of ongoing star formation embedded in cores of 0.2 pc
scales and $\gtrsim$10$^5$ cm$^{-3}$ densities. Among the five clouds, Sgr C
possesses a high (9%) fraction of gas mass in gravitationally bound and/or
protostellar cores, and follows the dense ($\gtrsim$10$^4$ cm$^{-3}$) gas star
formation relation that is extrapolated from nearby clouds. The other four
clouds have less than 1% of their cloud masses in gravitationally bound and/or
protostellar cores, and star formation rates 10 times lower than predicted by
the dense gas star formation relation. At the spatial scale of these cores, the
star formation efficiency is comparable to that in Galactic disk sources. We
suggest that the overall inactive star formation in these Central Molecular
Zone clouds could be because there is much less gas confined in gravitationally
bound cores, which may be a result of the strong turbulence in this region
and/or the very early evolutionary stage of the clouds when collapse has only
recently started.
