The effect of multiple features on the power spectrum in two-field inflation

We extend our previous work on the enhancement of the curvature spectrum during inflation to the two-field case. We identify the slow-roll parameter $\eta$ as the quantity that can trigger the rapid growth of perturbations. Its two components, $\eta_\parallel$ along the background trajectory and $\eta_\perp$ perpendicular to it, remain small during most of the evolution, apart from short intervals during which they take large, positive or negative, values. The typical reason for the appearance of strong features in $\eta_\parallel$ is sharp steps or inflection points in the inflaton potential, while $\eta_\perp$ grows large during sharp turns in field space. We focus on the additive effect of several features leading to the resonant growth of the curvature spectrum. Three or four features in the evolution of $\eta$ are sufficient in order to induce an enhancement of the power spectrum by six or seven orders of magnitude, which can lead to the significant production of primordial black holes and stochastic gravitational waves. A big part of our study focuses on understanding the evolution of the perturbations and the resulting spectra through analytic means. The presence of multiple features in the background evolution points to a more complex inflationary paradigm, which is also more natural in the multi-field case. The critical examination of this possibility is within the reach of experiment.