Acoustic gravitational waves from primordial curvature perturbations

TL;DR

This work addresses nonperturbative corrections to scalar-induced gravitational waves from primordial curvature perturbations by isolating the acoustic, fluid-driven GW channel. It introduces a hybrid approach that first uses fully GR, 1D simulations to extract nonperturbative sound-shell profiles and then embeds these profiles into 3D lattice simulations of relativistic hydrodynamics coupled to TT metric perturbations to compute the acoustic GW spectra. The results show that nonperturbative fluid dynamics can amplify acoustic GWs by orders of magnitude relative to perturbative SIGWs and shift the peak to lower frequencies, with the amplitude scaling steeply as $R_{*c}^{-7}$ and a robust $k^3$ infrared tail. These findings underscore the importance of nonlinear hydrodynamics in predicting stochastic GW backgrounds from small-scale primordial perturbations and highlight the need for fully nonperturbative 3D GR treatments in future work.

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 $R_{*c}^{-7}$. 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.

Figures (8)

• Figure 1: Density contrast (left column) and radial velocity (right column) at several time slices for subcritical ($\mu = 0.4$), negative-amplitude ($\mu=-0.4$), near-critical ($\mu = 0.8$), and supercritical ($\mu = 0.9$) perturbations (from top to bottom).
• Figure 2: Comparison of the density-contrast profiles from the Misner-Sharp simulations (solid lines) and linear evolution (dashed lines) at several time slices for $\mu = 0.001$ (a), $0.4$ (b), $-0.4$ (c), $0.8$ (d), and $0.9$ (e). Note that in panel (a), the solid and dashed lines coincide.
• Figure 3: Slices of $\tilde{T}^{00}$ from a representative simulation. The initial condition is constructed by embedding the 1D sound-shell profile with $\mu = 0.4$ at $t_i = 50t_m$; the box length is $\tilde{L} = 1200$, and the number of sound shells is $N_s = 400$. The four snapshots correspond to $\tilde{\eta} = 70.71$ (a), $\tilde{\eta} = 190.71$ (b), $\tilde{\eta} = 310.71$ (c), and $\tilde{\eta} = 550.71$ (d).
• Figure 4: GW energy spectra at several time slices for the subcritical case ($\mu=0.4$). Top row: $\tilde{L} = 600$, $N_s = 50$. Bottom row: $\tilde{L} = 2400$, $N_s = 3200$. Left panels use the nonlinear hydrodynamic equations, while right panels use the linearized hydrodynamics. The initial condition is constructed by the 1D sound-shell profile at $t_i = 50t_m$. The red dot-dashed lines show the semi-analytical results from the sound shell model, normalized to match the peak of the numerical spectra. The dashed vertical line marks $k = 4/d$, where $d$ is the comoving thickness of the shell. The blue reference line indicates the causal $k^3$ scaling in the IR regime.
• Figure 5: GW energy spectra at several time slices for negative-amplitude ($\mu = -0.4$, left), near-critical ($\mu = 0.8$, middle), and supercritical ($\mu = 0.9$, right) perturbations. Red dot-dashed lines represent the semi-analytical results using the sound shell model. Top row: representative small-box runs: $\tilde{L} = 600$, $1000$, and $1300$, respectively, with $N_s = 50$ sound shells. Bottom row: larger-box, higher-$N_s$ simulations used to confirm the IR scaling ($\tilde{L} = 2400$, $N_s = 3200$ for negative-amplitude; $\tilde{L} = 2000$, $N_s = 400$ for near-critical; $\tilde{L} = 5200$, $N_s = 3200$ for supercritical).