The persistent percolation of single-stream voids

We study the nature of voids defined as single-stream regions that have not undergone shell-crossing. We use ORIGAMI to determine the cosmic web morphology of each dark matter particle in a suite of cosmological $N$-body simulations, which explicitly calculates whether a particle has crossed paths with others along multiple sets of axes and does not depend on a parameter or smoothing scale. The theoretical picture of voids is that of expanding underdensities with borders defined by shell-crossing. We find instead that locally underdense single-stream regions are not bounded on all sides by multi-stream regions, thus they percolate, filling the simulation volume; we show that the set of multi-stream particles also percolates. This percolation persists to high resolution, where the mass fraction of single-stream voids is low, because the volume fraction remains high; we speculate on the fraction of collapsed mass in the continuum limit of infinite resolution. By introducing a volume threshold parameter to define underdense void "cores", we create a catalog of ORIGAMI voids which consist entirely of single-stream particles and measure their percolation properties, volume functions, and average densities.