Gravitational wave emission from nonspherical collapse in an early matter-dominated era using N-body simulations

We study the dynamics of the collapse of a nonspherical overdense patch during an early matter-dominated era and the associated production of gravitational waves (GWs) using a semirelativistic N-body framework that we develop. The collapsing patch is initialized through a Zel'dovich deformation of a homogeneous sphere and evolved in an Einstein--de Sitter background, while the emitted signal is computed directly from the numerical quadrupole evolution. We show that a reliable prediction of the signal requires a fully numerical treatment of the nonlinear collapse dynamics. In particular, fitting-based procedures and Zel'dovich-based estimates fail to capture the post-shell-crossing evolution and can over/under-estimate the emitted power of the GWs. After averaging over realizations weighted by the Doroshkevich and BBKS (peak theory) distributions, we find that the two spectra have similar shapes and remain within the same overall order of magnitude at the peak amplitude, although the BBKS result is systematically smaller. The dominant contribution arises from peaks of relatively modest height, around $\nu \simeq 3$, while a larger variance significantly enhances the signal. Finally, by varying the horizon mass and reheating temperature, we map the present-day GW spectra to the sensitivity bands of different classes of detectors. In this way, the signal can populate a broad range of frequencies, from pulsar timing arrays to very high-frequency experiments, showing that GWs from nonspherical collapse can provide a probe of the pre-BBN thermal history.