In the SSA22 field which exhibits a large-scale proto-cluster at z = 3.1, we carried out a spectroscopic survey for Lyman Break Galaxies (LBGs) with the VLT/VIMOS and identified 78 confident LBGs at z = 2.5-4. We stacked their spectra in the observer's frame by using a sophisticated method. Analysing the composite spectrum, we have revealed that the large-scale proto-cluster at z = 3.1 has a strong H i absorption dip of rest-frame equivalent width of-1.7 Å. Another strong absorption dip found at z = 3.28 is associated with a modestly high-density LBG peak, similar to that at z = 3.1. We have also detected an H i transparency peak at z = 2.98 in the composite spectrum, coincident with a void in the LBG distribution. In this paper, we also investigated the relation between LBGs, H i gas, and active galactic nuclei (AGNs) at z = 3-4 in the SSA22 field. Two AGNs at z = 3.353 and 3.801 are, respectively, associated with the LBG concentration of an overdensity factor δLBG â‰ 2 in the present statistics. Another structure at z = 3.453 is remarkable: 20 comoving Mpc-scale dense H i gas which is not associated with any apparent LBG overdensity but involving a pair of AGNs. Such structure may be a new type of the AGN-matter correlation. If the inhomogeneous structures over a comoving Gpc scale found in this paper are confirmed with sufficient statistics in the future, the SSA22 field will become a key region to test the standard cold dark matter structure formation scenario.
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