We discuss the cosmological dependence of the star formation history of the
universe, within the framework of a very simple semianalytic model, where
star formation occurs within the virialized cores of dark matter halos, at
a rate which is primarily governed by the rate of matter infall into the ha
lo core. Our model is extremely simple, contains a number of uncertain feat
ures, and cannot be expected to predict detailed properties of the galaxy d
istribution. In spite of these great uncertainties, we find that at suffici
ently high redshifts fundamental differences between cosmologies (and not u
ncertainties in the star formation model) are the dominant factor determini
ng star formation history. Consequently, we argue that observations of star
-forming galaxies at high redshift (z > 5) with telescopes such as the Next
Generation Space Telescope (NGST) can provide a powerful probe of cosmolog
y.