THE GREAT OBSERVATORIES ORIGINS DEEP SURVEY: CONSTRAINTS ON THE LYMAN CONTINUUM ESCAPE FRACTION DISTRIBUTION OF LYMAN-BREAK GALAXIES AT 3.4 < z < 4.5

We use ultra-deep ultraviolet VLT/VIMOS intermediate-band and VLT/FORS1 narrowband imaging in the GOODS Southern field to derive limits on the distribution of the escape fraction (f(esc)) of ionizing radiation for L >= L(z=3)* Lyman-break galaxies (LBGs) at redshift 3.4-4.5. Only one LBG, at redshift z = 3.795, is detected in its Lyman continuum (LyC; S/N similar or equal to 5.5), the highest redshift galaxy currently known with a direct detection. Its ultraviolet morphology is quite compact (R(eff) = 0.8 kpc physical). Three out of seven active galactic nuclei are also detected in their LyC, including one at redshift z = 3.951 and z(850) = 26.1. From stacked data (LBGs), we set an upper limit to the average f(esc) in the range 5%-20%, depending on how the data are selected (e. g., by magnitude and/or redshift). We undertake extensive Monte Carlo simulations that take into account intergalactic attenuation, stellar population synthesis models, dust extinction, and photometric noise in order to explore the moments of the distribution of the escaping radiation. Various distributions (exponential, log-normal, and Gaussian) are explored. We find that the median f(esc) is lower than similar or equal to 6% with an 84% percentile limit not larger than 20%. If this result remains valid for fainter LBGs down to current observational limits, then the LBG population might be not sufficient to account for the entire photoionization budget at the redshifts considered here, with the exact details dependent upon the assumed ionizing background and QSO contribution thereto. It is possible that f(esc) depends on the UV luminosity of the galaxies, with fainter galaxies having higher f(esc), and estimates of f(esc) from a sample of faint LBGs from HUDF (i775 <= 28.5) are in broad quantitative agreement with such a scenario