Questions on calculation of primordial power spectrum with large spikes: the resonance model case

Understand

Inflationary models predicting a scale-dependent large amplification of the density perturbations have recently attracted a lot of attention because the amplified perturbations can seed a sizable amount of primordial black holes (PBHs) and stochastic background of gravitational waves (GWs).

• While the power spectra in these models are computed based on the linear equation of motion, it is not obvious whether loop corrections are negligible when such a large amplification occurs during inflation.
• In this paper, as a first step to discuss the loop corrections in such models, we use the in-in formalism and calculate the one-loop scalar power spectrum numerically and analytically in an illustrative model where the density perturbations are resonantly amplified due to oscillatory features in the inflaton potential.
• Our calculation is technically new in that the amplified perturbations are numerically taken into account in the in-in formalism for the first time.