Cosmological hydrodynamic simulations have significantly improved over the past several years , and we have already shown that the observed properties of Lyman-break galaxies ( LBGs ) at z = 3 can be explained well by the massive galaxies in the simulations .
Here we extend our study to z = 6 and show that we obtain good agreement for the LBGs at the bright-end of the luminosity function ( LF ) .
Our simulations also suggest that the cosmic star formation rate density has a peak at z = 5 - 6 , and that the current LBG surveys at z = 6 are missing a significant number of faint galaxies that are dimmer than the current magnitude limit .
Together , our results suggest that the universe could be reionized at z = 6 by the Pop II stars in ordinary galaxies .

We also estimate the LF of Lyman- \alpha emitters ( LAEs ) at z = 6 by relating the star formation rate in the simulation to the Ly \alpha luminosity .
We find that the simulated LAE LFs agree with the observed data provided that the net escape fraction of Ly \alpha photon is f _ { Ly \alpha } \leq 0.1 .
We investigate two possible scenarios for this effect : ( 1 ) all sources in the simulation are uniformly dimmer by a factor of 10 through attenuation , and ( 2 ) one out of ten LAEs randomly lights up at a given moment .
We show that the correlation strength of the LAE spatial distribution can possibly distinguish the two scenarios .