We study the escape of Ly-alpha photons from Ly-alpha emitting galaxies (LAEs) and the overall galaxy population using a sample of 99 LAEs at 1.9<z<3.8 detected through integral-field spectroscopy of blank fields by the HETDEX Pilot Survey. For 89 LAEs showing counterparts in deep broad-band images we measure the rest-frame UV luminosity and the UV slope, which we use to estimate E(B-V) under the assumption of a constant intrinsic UV slope for LAEs. These two quantities are used to measure the dust-corrected star formation rate (SFR). A comparison between the observed Ly-alpha luminosity and that predicted by the dust-corrected SFR yields the Ly-alpha escape fraction. We also measure the Ly-alpha luminosity function. Integration of the luminosity function provides a measurement of the Ly-alpha luminosity density across our redshift range. We combine our data with that from other surveys at 0.3<z<7.7 to trace the evolution of the Ly-alpha luminosity density. We then compare it to that expected from the star-formation history of the universe in order to characterize the evolution of the Ly-alpha escape fraction of the overall galaxy population [abriged]
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