The first galaxies in the Universe are built up where cold dark matter ( CDM ) forms large scale filamentary structure .
Although the galaxies are expected to emit numerous Ly \alpha photons , they are surrounded by plentiful neutral hydrogen with a typical optical depth for Ly \alpha of \sim 10 ^ { 5 } ( H i halos ) before the era of cosmological reionization .
The H i halo almost follows the cosmological Hubble expansion with some anisotropic corrections around the galaxy because of the gravitational attraction by the underlying CDM filament .
In this paper , we investigate the detectability of the Ly \alpha emissions from the first galaxies , examining their dependence on viewing angles .
Solving the Ly \alpha line transfer problem in an anisotropically expanding H i halo , we show that the escape probability from the H i halo is the largest in direction along the filament axis .
If the Ly \alpha source is observed with a narrow-band filter , the difference of apparent Ly \alpha line luminosities among viewing angles can be a factor of \gtrsim 40 at an extreme case .
Furthermore , we evaluate the predicted physical features of the Ly \alpha sources and flux magnification by gravitational lensing effect due to clusters of galaxies along the filament .
We conclude that , by using the next generation space telescopes like the JWST , the Ly \alpha emissions from the first galaxies whose CDM filament axes almost face to us can be detected with the S/N of \gtrsim 10 .