Acoustic gravitational waves from primordial curvature perturbations

Abstract

Standard perturbative calculations of scalar-induced gravitational waves (SIGWs) have neglected nonperturbative effects in the large-amplitude regime. We develop a hybrid numerical framework to signify nonperturbative effects on the stochastic gravitational wave (GW) background sourced by primordial curvature perturbations, focusing on the acoustic channel (fluid motions). Fully general-relativistic, spherically symmetric simulations are used to extract nonperturbative sound-shell profiles from isolated curvature peaks; these profiles are then embedded into three-dimensional lattice evolutions of relativistic hydrodynamics coupled to transverse-traceless metric perturbations to compute the acoustic GW spectra. The acoustic signal has a peak frequency determined by the comoving shell thickness, and its amplitude is extremely sensitive to the mean comoving separation of peaks, scaling approximately as $R_{\ast c}^{-7}$. We find a robust causal low-frequency tail $\propto k^3$, and the nonlinear hydrodynamic interactions can enhance the ultraviolet power. Comparing with SIGWs computed perturbatively from the same real-space configuration, we show that acoustic GWs can be amplified by an order of magnitude and display a peak shifted to a lower frequency in the large-amplitude regime. These results highlight the importance of nonperturbative effects for accurate predictions of stochastic GW signals induced from primordial curvature perturbations.

Comments: 29 pages, 8 figures, a second companion paper (with direct numerical simulations for the acoustic gravitational waves) to the letter arXiv:2504.11275 and the long paper arXiv:2504.12243