Stochastic Gravitational Waves from Early Structure Formation

Early matter-dominated eras (EMDEs) are a natural feature arising in many models of the early universe and can generate a stochastic gravitational wave background (SGWB) during the transition from an EMDE to the radiation-dominated universe required by the time of Big Bang Nucleosynthesis. While there are calculations of the SGWB generated in the linear regime, no detailed study has been made of the nonlinear regime. We perform the first comprehensive calculation of GW production in the nonlinear regime, using a hybrid $N$-body and lattice simulation to study GW production from both a metastable matter species and the radiation produced in its decay. We find that nonlinearities significantly enhance GW production up to frequencies at least as large as the inverse light-crossing time of the largest halos that form prior to reheating. The resulting SGWB is within future observational reach for curvature perturbations as small as those probed in the cosmic microwave background, depending on the reheating temperature. Out-of-equilibrium dynamics could further boost the induced SGWB, while a fully relativistic gravitational treatment is required to resolve the spectrum at even higher frequencies.