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(NL), for models of inflation with a large peak in their primordial power spectra. We find f(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(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.

Automated summary

In this study, we work within an idealized framework to match a series of evolution phases defined by the second slow-roll parameter eta. We calculate the reduced bispectrum, f(NL), for inflation models with a significant peak in their primordial power spectra. Our findings show that f(NL) remains relatively constant over the scales where the peak is located, and we provide an analytic approximation for this value. Additionally, we identify the conditions under which f(NL) is large enough to have a significant impact on the production of primordial black holes (PBHs) and scalar induced gravitational waves (SIGWs). The analytic formulas for the gradient of the rise and fall in the power spectrum, along with these findings, offer a toolkit for designing or quickly analyzing inflationary models that generate PBHs and SIGWs.