One-dimensional gravity

The evolution of structure in the cosmos is a complicated process in which small-amplitude initial seed fluctuations in density are amplified by gravity. These then collapse to form bound structures which then may virialise and merge with other collapsed structures. The equations governing this are complicated and non-linear, and must be solved by computers and the resulting simulations analysed to try and glean understanding of the gravitatiaonl amplification processes. This is complicated in three dimensions because the phase space is six dimensional and cannot be visualised easily. A simplified example of collapse in only one spatial dimension is easier to analyse because the phase space is then only two dimensional. The movie shows the phase-space density of collapse of a series of these parallel sheets. The horizontal axis is position while the vertical axis is velocity. A higher density of sheets is indicated by whiter colours. By construction, any density in the upper half of the movie must be moving to the right and any density in the lower half must be moving to the left. As the collapse occurs the initial perturbed phase space forms spirals that then wind round themselves and each other as collapse progresses. The continuity of the phase space, and the constantcy of the phase-space density can be seen as, despite the chaotic behaviour, there are never any discontinuities and the density merely gets stretched, smeared and squashed. In the real collapse of cold dark matter in our three-dimensional Universe this type of phase space mixing and spirals are expect at all scales, but in six dimensions rather than just two.