With Monte Carlo simulation method , we investigate the time dependent behavior of Ly \alpha photon transfer in optically thick medium of the concordance \Lambda CDM universe .
At high redshift , the Ly \alpha photon escaping from optically thick medium has a time scale as long as the age of the luminous object , or even comparable to the age of the universe .
In this case , time-independent , or stationary solutions of the Ly \alpha photon transfer with resonant scattering will overlook important features of the escaped Ly \alpha photons in physical and frequency spaces .
More seriously , the expansion of the universe leads to that the time-independent solutions of the Ly \alpha photon transfer may not exist .
We show that time-dependent solutions sometimes are essential for understanding the Ly \alpha emission and absorption at high redshifts .
For Ly \alpha photons from sources at redshift 1 + z = 10 and being surrounded by neutral hydrogen IGM of the \Lambda CDM universe , the escape coefficient is found to be always less , or much less than one , regardless of the age or life time of the sources .
Under such environment , we also find that even when the Ly \alpha photon luminosity of the sources is stable , the mean surface brightness is gradually increasing in the first 10 ^ { 6 } years , and then decreasing with a power law of time , but never approaches a stable , time-independent state .
That is , all 1 + z = 10 sources in a neutral Hubble expanding IGM with Ly \alpha luminosity L have their maximum of mean surface brightness \sim 10 ^ { -21 } ( L / 10 ^ { 43 } { erg / s } ) erg s ^ { -1 } cm ^ { -2 } arcsec ^ { -2 } at the age of about 10 ^ { 6 } years .
The time-dependent effects on the red damping wing profile are also addressed .