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Identification of the Lyman break galaxies, by using the 912 Å discontinuity in predicted spectra as a broad band redshift indicator, has revolutionized our knowledge of early star formation. Current samples of high redshift star-forming galaxies, chosen in a relatively unbiased manner, contain ~ 1000 galaxies at z ~ 3 and ~ 100 galaxies at z ~ 4. The volume of the universe involved is known, and one can therefore compute the comoving luminosity density. 37 Since the galaxies are selected in the rest-frame UV, one can convert luminosity density to massive star formation rate. One uncertainty is correction for dust extinction but this is mostly resolved by measurement of the galaxy spectra.

If, say, a Miller-Scalo initial stellar mass function is adopted, one concludes that the star formation rate per unit volume rose rapidly between the present epoch and redshift unity by a factor of about 10. Beyond redshift one, the star formation rate remains approximately constant, to z > 4. Moreover the median star formation rate per galaxy is high, around 30 Msun per year, the star forming galaxies are mostly compact, and strong clustering is found. 38 One interpretation of the data is that most stars formed late, because of the short cosmic time available at high redshift, and that most of the Lyman-break galaxies are massive, and hence clustered, objects that are probably undergoing spheroid formation. An alternative view is that the clustering is due to merger-induced starbursts of low mass galaxies within massive galaxy halos. 39 Reconcilation of either interpretation with hierarchical clustering theory requires a low Omega universe, especially in the former case, and a detailed prescription for galaxy star formation. The rapid rise in the number of star-forming galaxies at low redshift is especially challenging if Omega is low, since galaxy clustering reveals little or no evolution at z ~lt 1, as measured by cluster abundances, and both massive disk sizes and the Tully-Fisher relation show little change to z ~ 1. One intersting suggestion is that a new population of blue compact, star-forming galaxies is responsible for the evolution in the star formation rate density of the universe. 40