Non-Gaussianity in inflationary scenarios for primordial black holes
  Working in an idealised framework in which a series of phases of evolution
defined by the second slow-roll parameter $\eta$ are matched together, we
calculate the reduced bispectrum, $f_{\rm NL}$, for models of inflation with a
large peak in their primordial power spectra. We find $f_{\rm NL}$ is typically
approximately constant over scales at which the peak is located, and provide an
analytic approximation for this value. This allows us to identify the
conditions under which $f_{\rm NL}$ is large enough to have a significant
impact on the resulting production of primordial black holes (PBHs) and scalar
induced gravitational waves (SIGWs). Together with analytic formulae for the
gradient of the rise and fall in the power spectrum, this provides a toolkit
for designing or quickly analysing inflationary models that produce PBHs and
SIGWs.
