We present results from a blind , spectroscopic search for redshift 5.7 Ly \alpha emission-line galaxies at Keck I .
Using a band-limiting filter and custom slitmask , we cover the LRIS detector with low resolution spectra in the 8100 - 8250 \mbox { ~ { } \AA } atmospheric window which contains no bright night sky emission lines .
We find nine objects with line fluxes greater than our flux limit of 6 \times 10 ^ { -18 } ergs s ^ { -1 } cm ^ { -2 } in our \sim 5.1 square arcminute field .
We rule out a Ly \alpha identification for six of these based on the absence of the continuum break , expected at rest-1215 Å for high-z galaxies , and/or the identification of additional emission-lines in our follow-up spectra .
We find that extremely metal-poor , foreground emission-line galaxies are the most difficult type of interloper to recognize .
For the three remaining emission-line objects , we identify a plausible counterpart for each object in a deep V-band image of the field suggesting that none of them has a continuum break in the i band .
Our preliminary conclusion is that our field contains no z=5.7 Ly \alpha emitters brighter than 0.6 \mbox { $L ^ { * } _ { Ly \alpha } $ } , where \mbox { $L ^ { * } _ { Ly \alpha } $ } \equiv 3.26 \times 10 ^ { 42 } ergs s ^ { -1 } .
Selecting a field with zero Ly \alpha emitters is marginally consistent with the no-evolution hypothesis – i.e .
we expected to recover 2 to 3 Ly \alpha emitters assuming the Ly \alpha luminosity function at redshift 5.7 is the same as it is at redshift 3 .
Our null result rules out a brightening of L ^ { * } _ { Ly \alpha } by more than a factor of 1.7 from redshift 3 to redshift 5.7 , or , over the same redshift interval , an increase of more than a factor of 2.2 in the number density of Ly \alpha emitters .
The paucity of z=5.7 Ly \alpha emitters raises the question of whether the Ly \alpha -selected population plays a significant role in maintaining the ionization of the intergalactic medium at z = 5.7 .
We find that if the escape fraction of Ly \alpha radiation is less than 0.4 f _ { LyC } , where f _ { LyC } is the escape fraction of Lyman continuum photons , then the star formation rate in the Ly \alpha emitting population is high enough in the no-evolution model ( our upper limit ) to maintain the ionization of the IGM at z=5.7 .