  To demonstrate the feasibility of studying the epoch of massive galaxy
cluster formation in a more systematic manner using current and future galaxy
surveys, we report the discovery of a large sample of proto-cluster candidates
in the 1.62 deg^2 COSMOS/UltraVISTA field traced by optical/IR selected
galaxies using photometric redshifts. By comparing properly smoothed 3D galaxy
density maps of the observations and a set of matched simulations incorporating
the dominant observational effects (galaxy selection and photometric redshift
uncertainties), we first confirm that the observed ~15 comoving Mpc scale
galaxy clustering is consistent with LCDM models. Using further the relation
between high-z overdensity and the present day cluster mass calibrated in these
matched simulations, we found 36 candidate structures at 1.6<z<3.1, showing
overdensities consistent with the progenitors of M_z=0 ~10^15 M_sun clusters.
Taking into account the significant upward scattering of lower mass structures,
the probabilities for the candidates to have at least M_z=0 ~10^14 M_sun are
~70%. For each structure, about 15%-40% of photometric galaxy candidates are
expected to be true proto-cluster members that will merge into a cluster-scale
halo by z=0. With solely photometric redshifts, we successfully rediscover two
spectroscopically confirmed structures in this field, suggesting that our
algorithm is robust. This work generates a large sample of uniformly-selected
proto-cluster candidates, providing rich targets for spectroscopic follow-up
and subsequent studies of cluster formation. Meanwhile, it demonstrates the
potential for probing early cluster formation with upcoming redshift surveys
such as the Hobby-Eberly Telescope Dark Energy Experiment and the Subaru Prime
Focus Spectrograph survey.

Cosmology and Nongalactic Astrophysics