1202.3364 (Mark C. Neyrinck)

Origami constraints on the initial-conditions arrangement of dark-matter caustics and streams    [PDF]

Mark C. Neyrinck

In a cold-dark-matter universe, cosmological structure formation proceeds in rough analogy to origami folding. Dark matter occupies a three-dimensional 'sheet,' non-intersecting in six-dimensional velocity-position phase space. At early times, the sheet was flat like an origami sheet, i.e. velocities were essentially zero. The present paper further illustrates this analogy, and identifies a result of origami mathematics that applies to cosmology. We define caustics in the initial conditions Lagrangian space) as surfaces in this sheet, along which the sheet has folded. The regions outlined by these caustics, which we call streams, may be colored according to the two possible orientations of initial basis vectors, a two-coloring such that adjacent streams are not colored the same. While this may not have clear observational consequences, it is a severe restriction on connectivity, since there are no bounds on the number of colors required to color a general arrangement of three-dimensional regions. Then, measuring the relevant quantities from N-body simulations, we explore how well outer caustics in Lagrangian space correspond to a Zel'dovich prediction, as well as to a measurement from the recent ORIGAMI algorithm.

View original: http://arxiv.org/abs/1202.3364