Determine gravitational-wave and curvature-perturbation production from inflationary parametric amplification

Determine the gravitational-wave amplitude and spectrum, together with the associated curvature perturbations, generated by nonlinear parametric amplification of the PQ field during inflation, using a lattice simulation of the coupled inflaton, PQ-field, and metric-perturbation dynamics.

Background

The rolling PQ field can resonantly amplify fluctuations during inflation. These fluctuations may source gravitational waves directly through anisotropic stress and may also produce localized curvature perturbations that later generate scalar-induced gravitational waves when the modes re-enter the horizon.

The paper does not calculate these signals. The authors state that the relevant inflationary dynamics have not been studied in sufficient detail and call for a nonlinear lattice treatment that consistently includes the inflaton, PQ field, and metric perturbations.

References

To the best of our knowledge, however, the corresponding dynamics associated with parametric amplification of a scalar field during inflation has not yet been investigated in detail. A reliable determination of the resulting GW amplitude and spectrum, as well as the associated curvature perturbations, requires a dedicated nonlinear lattice simulation that consistently accounts for the coupled evolution of the inflaton, the PQ field, and metric perturbations. We leave such an analysis for future work.

— A Stepping Stone Solution to the QCD Axion Isocurvature Problem  (2609.28840 - Lyu et al., 23 Sep 2026) in Section 5, Transition Dynamics and Open Issues