  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.
