  We investigate charge fluctuations in the two-dimensional Hubbard model as a
function of doping, interaction strength, next-nearest-neighbor hopping, and
temperature within the eight-site dynamical cluster approximation. In the
regime of intermediate interaction strengths, we find that $d$ density wave
fluctuations, which had previously been postulated using analytical arguments,
are present and strong but cannot be interpreted as the cause of the pseudogap
in the model, due to their evolution with doping and interaction strength. For
all parameters away from half filling, the charge fluctuations investigated,
including $d$ density wave fluctuations, are weaker than $d$-wave
superconducting fluctuations.
