Scalar-induced gravitational waves including isocurvature perturbations with lattice simulations

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.