Comments on non-Gaussian density perturbations and the production of primordial black holes

We review the basic arguments for the likelihood of non-Gaussian density perturbations in inflation models with primordial black hole (PBH) production. We discuss our derived distributions of field fluctuations and their implications, specifically commenting on the fine-tuning problem. We also discuss how the derived distributions may be affected when linked to metric perturbations. While linking the metric perturbations to field fluctuations in a nonlinear way may be important for determining exact probability distributions, the correct mapping is not self-evident. The calculation of P. Ivanov, which yields skew positive distribution, is based on an ansatz for the behavior of the nonlinear metric perturbation. We note that the ``natural'' generalization of the gauge-invariant formalism favored by Bond and Salopek yields an effective linear link between the distribution of field fluctuations and metric perturbations during inflation.