  We use simple analytic reasoning to identify physical processes that drive
the evolution of the cosmic star formation density in cold dark matter
universes. Based on our analysis, we formulate a model to characterise the
redshift dependence of the star formation history and compare it to results
obtained from a set of hydrodynamic simulations which include star formation
and feedback. At early times, densities are sufficiently high and cooling times
sufficiently short that abundant quantities of star-forming gas are present in
all dark matter halos that can cool by atomic processes. Consequently, the star
formation density generically rises exponentially as z decreases, independent
of the details of the physical model for star formation, but dependent on the
normalisation and shape of the cosmological power spectrum. This part of the
evolution is dominated by gravitationally driven growth of the halo mass
function. At low redshifts, densities decline as the universe expands to the
point that cooling is inhibited, limiting the amount of star-forming gas
available. We find that in this regime the star formation rate scales
approximately in proportion to the cooling rate within halos. We derive
analytic expressions for the full star formation history and show that they
match our simulation results to better than ~10%. Using various approximations,
we reduce the expressions to a simple analytic fitting function that can be
used to compute global cosmological quantities that are directly related to the
star formation history. As examples, we consider the integrated stellar
density, the supernova and gamma-ray burst rates observable on Earth, the metal
enrichment history of the Universe, and the density of compact objects.
(abridged)
