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

TL;DR

This paper explores the origami-like folding of dark matter in the universe, revealing that the initial conditions constrain the arrangement of cosmic streams to only two colors, with implications for understanding cosmic structure formation.

Contribution

It demonstrates that dark matter streams can be colored with only two colors based on parity, imposing new constraints on their arrangement in Lagrangian space.

Findings

Streams are two-colorable based on local volume parity.

Caustics correspond to boundaries of cosmic structures like haloes and filaments.

Outer caustics align well with Zel'dovich-approximation predictions.

Abstract

In a cold-dark-matter universe, cosmological structure formation proceeds in rough analogy to origami folding. Dark matter occupies a three-dimensional 'sheet' of free- fall observers, 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, but as time passes, the sheet folds up to form cosmic structure. The present paper further illustrates this analogy, and clarifies a Lagrangian definition of caustics and streams: caustics are two-dimensional surfaces in this initial sheet along which it folds, tessellating Lagrangian space into a set of three-dimensional regions, i.e. streams. The main scientific result of the paper is that streams may be colored by only two colors, with no two neighbouring streams (i.e. streams on either side of a caustic surface) colored the same. The two colors correspond to positive and negative parities of local Lagrangian volumes. This is a severe restriction on the connectivity and therefore arrangement of streams in Lagrangian space, since arbitrarily many colors can be necessary to color a general arrangement of three-dimensional regions. This stream two-colorability has consequences from graph theory, which we explain. Then, using N-body simulations, we test how these caustics correspond in Lagrangian space to the boundaries of haloes, filaments and walls. We also test how well outer caustics correspond to a Zel'dovich-approximation prediction.