  We systematically study, in the context of the standard cold dark matter
model, star-formation suppression effects of two important known physical
processes---photoheating due to reionization of the intergalactic medium and
gravitational shock heating due to formation of massive halos and large-scale
structure---on the global evolution of star formation rate (SFR) density and
the so-called cosmic downsizing phenomenon in the redshift range z=0-6. We show
that the steep decline of cosmic SFR density from z~2 to z=0 can be primarily
explained by gravitational shock heating in two forms: massive halo
self-quenching and hot environment. Simultaneously, we show a decreasing trend
in the average SFR of star-forming galaxies from z=2 to z=0, reproducing the
observed cosmic downsizing at z<2. Nevertheless, the average halo mass of
star-forming galaxies is found to continue upsizing from z=2 to z=0. In stark
contrast to z<2, both photoheating and gravitational shock heating effects are
found to play a minor role in suppressing star formation. Additional negative
feedback effects are required to reconcile our model with observations at z>2.
Internal feedback from stellar evolution and supermassive black hole growth are
the natural candidates for this role, as galaxies at z>2 are more moderate in
mass but stronger in star formation and are thus more vulnerable. Our physical
model can be used to treat star formation in cosmological N-body simulations.
