We investigate the effects of the change of cosmological parameters and star formation (SF) models on the cosmic SF history using cosmological smoothed particle hydrodynamics (SPH) simulations based on the cold dark matter (CDM) model. We vary the cosmological parameters within 1-sigma error from the WMAP best-fit parameters, and find that such changes in cosmological parameters mostly affect the amplitude of the cosmic SF history. At high redshift (hereafter high-z), the star formation rate (SFR) is sensitive to the cosmological parameters that control the small-scale power of the primordial power spectrum, while the cosmic matter content becomes important at lower redshifts. We also test two new SF models: 1) the `Pressure model based on the work by Schaye & Dalla Vecchia (2008), and 2) the `Blitz model that takes the effect of molecular hydrogen formation into account, based on the work by Blitz & Rosolowsky (2006). Compared to the previous conventional SF model, the Pressure model reduces the SFR in low-density regions and shows better agreement with the observations of the Kennicutt-Schmidt law. This model also suppresses the early star formation and shifts the peak of the cosmic SF history toward lower redshift, more consistently with the recent observational estimates of cosmic SFR density. The simulations with the new SF model also predict lower global stellar mass densities at high-z, larger populations of low-mass galaxies and a higher gas fraction in high-z galaxies. Our results suggest that there is room left in the model uncertainties to reconcile the discrepancy that was found between the theory and observations of cosmic SF history and stellar mass density. Nevertheless, our simulations still predict higher stellar mass densities than most of the observational estimates.
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