Topology and geometry of the dark matter web

Topological connections in the single-streaming voids and multistreaming filaments and walls reveal a cosmic web structure different from traditional mass density fields. A single void structure not only percolates the multistream field in all the directions, but also occupies over 99 per cent of all the single-streaming regions. Sub-grid analyses on scales smaller than simulation resolution reveal tiny pockets of voids that are isolated by membranes of the structure. For the multistreaming excursion sets, the percolating structure is significantly thinner than the filaments in over-density excursion approach. Hessian eigenvalues of the multistream field are used as local geometrical indicators of dark matter structures. Single-streaming regions have most of the zero eigenvalues. Parameter-free conditions on the eigenvalues in the multistream region may be used to delineate primitive geometries with concavities corresponding to filaments, walls and haloes.