  The detection of primordial non-Gaussianity could provide a powerful means to
test various inflationary scenarios. Although scale-invariant non-Gaussianity
(often described by the $f_{NL}$ formalism) is currently best constrained by
the CMB, single-field models with changing sound speed can have strongly
scale-dependent non-Gaussianity. Such models could evade the CMB constraints
but still have important effects at scales responsible for the formation of
cosmological objects such as clusters and galaxies. We compute the effect of
scale-dependent primordial non-Gaussianity on cluster number counts as a
function of redshift, using a simple ansatz to model scale-dependent features.
We forecast constraints on these models achievable with forthcoming data sets.
We also examine consequences for the galaxy bispectrum. Our results are
relevant for the Dirac-Born-Infeld model of brane inflation, where the
scale-dependence of the non-Gaussianity is directly related to the geometry of
the extra dimensions.
