Employing hydrodynamic simulations of structure formation in a LCDM cosmology, we study the history of cosmic star formation from the dark ages at redshift z~20 to the present. In addition to gravity and ordinary hydrodynamics, our model includes radiative heating and cooling of gas, star formation, supernova feedback, and galactic winds. By making use of a comprehensive set of simulations on interlocking scales and epochs, we demonstrate numerical convergence of our results on all relevant halo mass scales, ranging from 10^8 to 10^15 Msun/h. The predicted density of cosmic star formation is broadly consistent with measurements, given observational uncertainty. From the present epoch, it gradually rises by about a factor of ten to a peak at z~5-6, which is beyond the redshift range where it has been estimated observationally. 50% of the stars are predicted to have formed by redshift z~2.1, and are thus older than 10.4 Gyr, while only 25% form at redshifts lower than z~1. The mean age of all stars at the present is about 9 Gyr. Our model predicts a total stellar density at z=0 of Omega_*=0.004, corresponding to about 10% of all baryons being locked up in long-lived stars, in agreement with recent determinations of the luminosity density of the Universe. We determine the multiplicity function of cosmic star formation as a function of redshift; i.e. the distribution of star formation with respect to halo mass. We also briefly examine possible implications of our predicted star formation history for reionisation of hydrogen in the Universe. We find that the star formation rate predicted by the simulations is sufficient to account for hydrogen reionisation by z~6, but only if a high escape fraction close to unity is assumed. (abridged)
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