Non-Gaussianity in inflationary scenarios for primordial black holes

Understand

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.