  The cosmic star formation rate is observed to drop sharply after redshift
z=2. We use a large, cosmological, smoothed particle hydrodynamics simulation
to investigate how this decline is related to the evolution of gas accretion
and to outflows driven by active galactic nuclei (AGN). We find that the drop
in the star formation rate follows a corresponding decline in the global
cold-mode accretion rate density onto haloes, but with a delay of order the gas
consumption time scale in the interstellar medium. Here we define cold-mode
(hot-mode) accretion as gas that is accreted and whose temperature has never
exceeded (did exceed) 10^5.5 K. In contrast to cold-mode accretion, which peaks
at z~3, the hot mode continues to increase to z~1 and remains roughly constant
thereafter. By the present time, the hot mode strongly dominates the global
accretion rate onto haloes. Star formation does not track hot-mode halo
accretion because most of the hot halo gas never accretes onto galaxies. AGN
feedback plays a crucial role by preferentially preventing gas that entered
haloes in the hot mode from accreting onto their central galaxies.
Consequently, in the absence of AGN feedback, gas accreted in the hot mode
would become the dominant source of fuel for star formation and the drop off in
the cosmic star formation rate would be much less steep.
