A Flat Photoionization Rate at 2<z<4.2: Evidence for a Stellar-Dominated UV Background and Against a Decline of Cosmic Star Formation Beyond z~3

We investigate the implications of our measurement of the Lyman-alpha forest opacity at redshifts 2<z<4.2 from a sample of 86 high-resolution quasar spectra for the evolution of the cosmic ultraviolet luminosity density and its sources. The derived hydrogen photoionization rate is remarkably flat over this redshift range, implying an increasing comoving ionizing emissivity with redshift. Because the quasar luminosity function is strongly peaked near z~2, star-forming galaxies likely dominate the ionizing emissivity at z>~3. Our measurement argues against a star formation rate density declining beyond z~3, in contrast with existing state-of-the-art determinations of the cosmic star formation history from direct galaxy counts. Stellar emission from galaxies therefore likely reionized the Universe.