Cosmological consequences of Population III stars

We examine the possible cosmological consequences of Population III stars. Their dark remnants could provide the ''missing mass.'' Their light could have produced either the entire 3 K background or observable distortions in its spectrum. Their heat or explosions could have reionized the universe and perhaps produced galaxies. Their helium yield could suffice to provide an alternative explanation for the observed ''primordial'' abundance, and their heavy-element yield could have produced a burst of pregalactic enrichment. We discuss which sort of stars could best fulfill these roles and conclude that the most plausible candidates would be ''Very Massive Objects'' in the mass range 10/sup 2/--10/sup 5/ M/sub sun/. Even if Population III stars played none of these roles, consideration of the associated effects places strong constraints on their mass spectrum and formation epoch.