  Ly$\alpha$ line emission from the Loeb-Rybicki (LR) halo, which is the
expanding HI IGM (intergalactic medium) around the first star clusters and the
ionized interstellar medium, is investigated by solving a radiative transfer
problem. While the initial scattering optical depth is $\sim 10^5$ for the
Ly$\alpha$ photons, most of the Ly$\alpha$ photons can escape when the
cumulative frequency-shift due to the expansion of the HI IGM becomes
significantly large. The current paper improves upon previous treatments of the
scattering processes and the opacity for the Ly$\alpha$ transfer. Confirming
the previous results of the LR halo, we investigate the effect of the
aspherical expansion of the IGM. The asphericity is hypothesized to follow the
initial stage of the gravitational deceleration to form the large scale
filamentary structure of the Universe. According to our results, the effect of
the asphericity lets the peak wavelength of the line profile shift to longer
wavelengths and the FWHM of the profile become wider than those of the
spherically expanding model. To detect these features is meaningful if we are
interested in the initial evolution of the large scale structure, since they
reflect the dynamical properties of the IGM at that time. Furthermore, given
the recent discovery of the high redshift cosmological reionization, we briefly
comment on the effects of the redshift and the cosmological parameters on the
line profile.
