Scalar-induced gravitational waves including isocurvature perturbations with lattice simulations

TL;DR

This work investigates scalar-induced gravitational waves (SIGWs) generated by isocurvature perturbations using lattice simulations that handle mixed initial conditions. It validates pure isocurvature results against semi-analytical predictions, reveals that multi-peak structures persist similarly to adiabatic cases, and demonstrates how energy transfer during early matter domination, such as from primordial black holes or solitons, shapes the peak amplitude and slope depending on microphysical properties. The lattice approach provides a robust, nonperturbative framework for predicting SIGW spectra in complex primordial scenarios, with implications for interpreting current and future gravitational-wave observations. Overall, the paper extends SIGW theory beyond adiabatic perturbations and offers practical insights for connecting early-universe microphysics to observable GW signals.

Abstract

Scalar-induced gravitational waves (SIGWs) open a unique window into early-universe physics. While their generation from adiabatic perturbations has been extensively studied, the contribution from isocurvature perturbations remains poorly understood. In this work, we develop a lattice simulation framework to compute the stochastic gravitational wave background from both pure isocurvature and mixed initial conditions. Our numerical results show excellent agreement with semi-analytical predictions in the pure isocurvature case. We further analyze multi-peak structures under general initial conditions and find that they closely match those produced in purely adiabatic scenarios. Additionally, we examine SIGWs in early matter-dominated eras, revealing that the peak amplitude and spectral slope are sensitive to the microphysical properties of the dominant field, such as the primordial black hole mass, abundance, or soliton decay rate. This study establishes lattice simulations as a robust tool for predicting SIGW spectra from complex primordial perturbations, with important implications for interpreting current and future gravitational wave observations.

Figures (6)

• Figure 1: This figure compares the energy spectra of gravitational waves obtained via lattice simulation and semi-analytical methods. Solid lines correspond to semi-analytical results, and dashed curves represent lattice simulation outcomes. The initial amplitude of the isocurvature perturbation is $B=100$, while the peak scale is chosen as $k_*=30$. On the left panel, the matter-radiation equality parameter from Eq. \ref{['eq:ana_a']} is set to $\tau_* = 100$; on the right panel, $\tau_* = 10$.
• Figure 2: Peak structures for the isocurvature case (left) and the mixed initial condition case(right). Left: Semi-analytical results for the peak structure in the pure isocurvature scenario. Two representative cases are presented: $k_2 = 3k_1$ (three distinct peaks) and $k_2 = 4k_1$ (two peaks). Right: Lattice simulation results for the mixed initial condition, shown for different values of $\tau_*$ and $k_2/k_1$. Here, $k_1=20$ denotes the peak scale of the adiabatic perturbation, and $k_2$ the peak scale of the isocurvature perturbation. The width of power spectrum has been set as $\Delta_{\mathrm{ad}} = \Delta_{\mathrm{iso}}=1/30$.
• Figure 3: Left: The GWs energy spectra sourced by PBH isocurvature perturbations. We have set $k_{\mathrm{UV}} = 40$ in our simulations. Right: The energy density fraction $\Omega_i = \rho_{i=m,r}/(\rho_m+\rho_r)$ of PBH and radiation. The dashed lines denote $\Omega_m$, while the solid line describes $\Omega_r$. $t$ is the cosmic time.
• Figure 4: Left: The GWs energy spectra sourced by PBH isocurvature perturbations for different PBH masses. Right: The GWs energy spectra sourced by PBH isocurvature perturbations for different PBH abundances. In both figures, we have multiplied a constant to make their ultraviolet part the same.
• Figure 5: Left: The GWs energy spectra sourced by Q-balls isocurvature perturbations. We have set $k_{\mathrm{UV}} = 40$ in our simulations. Right: The energy density fraction $\Omega_i = \rho_{i=m,r}/(\rho_m+\rho_r)$ of Q-balls and radiation. The dashed lines denote $\Omega_m$, while the solid line describes $\Omega_r$. $t$ is the cosmic time. The initial abundance is set as $\beta = 5\times 10^{-2}$.