This paper explains a simple and robust way to amplify small-scale primordial fluctuations during inflation. The authors show that when inflation proceeds in two stages along different field directions, and the second stage is at a much lower energy, the path in field space can make a sharp transition with a series of rapid turns. Fluctuations that cross the Hubble horizon while the fields are turning can grow by many orders of magnitude.

The researchers study a minimal model of two scalar fields with ordinary (canonical) kinetic energy and a simple potential. The reference potential they use is V(χ,ψ) = m_χ^2 χ^2 + m_ψ^2 ψ^2 + c_w ψ^2(χ − χ0)^2, which has two valleys and naturally produces two stages of inflation. If the system starts away from the lower valley it oscillates in the perpendicular field while rolling down the main direction. Those oscillations produce repeated bends in the background trajectory without needing a finely tuned potential.

At a technical level, the effect works through the coupling between curvature (adiabatic) perturbations and isocurvature (entropy) perturbations. During a sharp turn, the effective mass of the isocurvature fluctuation can briefly become negative (a tachyonic instability). That makes the isocurvature mode grow quickly. Because the two modes are coupled during turning, the growing isocurvature perturbations source the curvature perturbation. When the turns end, the curvature perturbation freezes at a larger amplitude. The authors call this process “assisted enhancement.”

This local amplification produces a prominent peak in the scalar power spectrum at small scales. Such a peak can have observable consequences well away from the cosmic microwave background (CMB) window. In particular, it can increase the abundance of primordial black holes (PBHs) and produce a stochastic background of scalar-induced gravitational waves (SIGWs). The paper notes that the associated SIGW background can fall within sensitivity ranges of pulsar timing array experiments and future space-based gravitational-wave detectors.