Gravitational Waves from Collapse of Pressureless Matter in the Early Universe

If an early matter phase of the Universe existed after inflation with the proper power spectrum, enhanced density perturbations can decouple from the Hubble flow, turn around and collapse. In contrast to what happens in a radiation dominated Universe where pressure nullifies deviations from sphericity in these perturbations, in a matter dominated Universe, the lack of pressure although on the one hand facilitates the gravitational collapse, it allows small deviations from sphericity to grow substantially as the collapse takes place. The subsequent collapse is complicated: initially as non-spherical deviations grow, the collapsing cloud takes the form of a ``Zel'dovich pancake". After that, the more chaotic and nonlinear stage of violent relaxation begins where shells of the cloud cross and the matter is redistributed within a factor of a few of the free fall timescale, reaching a spherical virialized state. During the whole process, strong gravitational waves are emitted due to the anisotropy of the collapse and the small time interval that the effect takes place. The emission of gravitational waves during the stage of the violent relaxation cannot be easily estimated with an analytical model. We perform an $N$-body simulation to capture the behaviour of matter during this stage in order to estimate the precise spectrum of gravitational waves produced in this scenario.