If the Universe is dominated by cold dark matter and dark energy as in the currently popular CDM cosmology, it is expected that large scale structures form gradually, with galaxy clusters of mass M & 1014M⊙ appearing at around 6 Gyrs after the Big Bang (z ∼ 1). Here, we report the discovery of 59 massive structures of galaxies with masses greater than a few times 1013M⊙ at redshifts between z = 0.6 and 4.5 in the Great Observatories Origins Deep Survey fields. The massive structures are identified by running top-hat filters on the two dimensional spatial distribution of magnitude-limited samples of galaxies using a combination of spectroscopic and photometric redshifts. We analyze the Millennium simulation data in a similar way to the analysis of the observational data in order to test the CDM cosmology. We find that there are too many massive structures (M > 7×1013M⊙) observed at z > 2 in comparison with the simulation predictions by a factor of a few, giving a probability of < 1/2500 of the observed data being consistent with the simulation. Our result suggests that massive structures have emerged early, but the reason for the discrepancy with the simulation is unclear. It could be due to the limitation of the simulation such as the lack of key, unrecognized ingredients (strong non-Gaussianity or other baryonic physics), or simply a difficulty in the halo mass estimation from observation, or a fundamental problem of the CDM cosmology. On the other hand, the over-abundance of massive structures at high redshifts does not favor heavy neutrino mass of ∼ 0.3 eV or larger, as heavy neutrinos make the discrepancy between the observation and the simulation more pronounced by a factor of 3 or more.

Abstract
1. INTRODUCTION
2. DATA
    2.1. Imaging Data and Catalog
    2.2. Spectroscopic Redshifts
3. PHOTOMETRIC REDSHIFTS AND SED FITTING
4. MSGS IN GOODS FIELDS
    4.1. Search Method
    4.2. MSGs in GOODS Fields
    4.3. Mass of MSGs
    4.4. Comparison with Previously Identified (Proto-)Clusters in GOODS Fields
5. ANALYSIS OF MILLENNIUM SIMULATION DATA
6. NUMBER DENSITY OF MSGS
7. DISCUSSION
    7.1. Cosmic Variance
    7.2. Implications for Initial Density Fluctuations
    7.3. Constraints on Hot Dark Matter
    7.4. Why Are There Too Many MSGs at z>2?
8. CONCLUSIONS
REFERENCES

• Eugene Kang(CEOU, Astronomy Program, Department of Physics and Astronomy, Seoul National University/Korea Educational Broadcasting System)
• Myungshin Im(CEOU, Astronomy Program, Department of Physics and Astronomy, Seoul National University) Corresponding author