Number Counts and Non-Gaussianity
  We describe a general procedure for using number counts of any object to
constrain the probability distribution of the primordial fluctuations, allowing
for generic weak non-Gaussianity. We apply this procedure to use limits on the
abundance of primordial black holes and dark matter ultracompact minihalos
(UCMHs) to characterize the allowed statistics of primordial fluctuations on
very small scales. We present constraints on the power spectrum and the
amplitude of the skewness for two different families of non-Gaussian
distributions, distinguished by the relative importance of higher moments.
Although primordial black holes probe the smallest scales, ultracompact
minihalos provide significantly stronger constraints on the power spectrum and
so are more likely to eventually provide small-scale constraints on
non-Gaussianity.
