Cosmological Origami: Properties of Cosmic-Web Components when a Non-Stretchy Dark-Matter Sheet Folds

Abstract: In the current cosmological paradigm, an initially flat three-dimensional manifold that pervades space (the dark-matter sheet') folds up to build concentrations of mass (galaxies), and a cosmic web between them. Galaxies are nodes, connected by a network of filaments and walls. The folding is in six-dimensional (3D position, plus 3D velocity) phase space. The positions of creases, or caustics, mark the edges of structures. Here, I introduce an origami approximation to cosmological structure formation, in which the dark-matter sheet is not allowed to stretch. But it still produces an idealized cosmic web, with nodes, filaments, walls and voids. In 2D, nodes form inpolygonal collapse' (a twist-fold in origami), necessarily generating filaments simultaneously. In 3D, nodes form in polyhedral collapse,' simultaneously generating filaments and walls. The masses, spatial arrangement, and angular momenta of nodes and filaments are related in the model. I describe sometetrahedral collapse', or tetrahedral twist-fold, models.