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.
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