We address the effects of cosmological surface brightness dimming on observations of faint galaxies by examining the distribution of "unobscured" star formation rate intensities versus redshift. We use the star formation rate intensity distribution function to assess the ultraviolet luminosity density versus redshift, based on our photometry and photometric redshift measurements of faint galaxies in the HDF and the HDF--S WFPC2 and NICMOS fields. We find that (1) previous measurements have missed a dominant fraction of the ultraviolet luminosity density of the universe at high redshifts by neglecting cosmological surface brightness dimming effects, which are important at redshifts larger than z = 2, (2) the incidence of the highest intensity star forming regions increases monotonically with redshift, and (3) the ultraviolet luminosity density plausibly increases monotonically with redshift through the highest redshifts observed. By measuring the spectrum of the luminosity density versus redshift, we also find that (4) previous measurements of the ultraviolet luminosity density at redshifts z < 2 must be reduced by a factor 2 to allow for the spectrum of the luminosity density between rest-frame wavelengths 1500 and 2800 A. And by comparing with observations of high-redshift damped Lyman-alpha absorption systems detected toward background QSOs, we further find that (5) the distribution of star formation rate intensities matches the distribution of neutral hydrogen column densities at redshifts z = 2 through 5, which establishes a quantitative connection between high-redshift galaxies and high column density gas and suggests that high-redshift damped Lyman-alpha absorption systems trace lower star formation rate intensity regions of the same galaxies detected in star light in the HDF and HDF--S.

28 pages, 9 figures; accepted for publication in the Astrophysical Journal