From chaos to cosmology: insights gained from 1D gravity

Abstract The gravitational force controls the evolution of Universe on several scales. It is responsible for formation galaxies from primordial matter distribution and planets solar nebulae. Because singular has infinite range, making predictions based fully three-dimensional models may be challenging. One-dimensional (1D) Newtonian gravity were proposed as toy understanding dynamics systems. They can integrated exactly used computer simulations starting in 1960s, providing first demonstration violent relaxation rapid development long-lived quasi-stationary states (QSS). present review provides bases physics 1D divided into two main parts, concerning approach to equilibrium second applications cosmology. Each part self-contained read independently other. In part, we provide an introduction thermodynamics one-dimensional sheet (OGS) system Vlasov limit. Both fixed periodic boundary conditions are considered. OGS studied through numerical which establish role played by QSS relaxation. We also survey existing work Lyapunov exponents chaotic systems with few particles, focusing three-body problem. summarizes dynamical structure cosmology using By transforming comoving coordinates, follow global expansion Universe, a useful laboratory studying various cosmological scenarios, Einstein-de Sitter ΛCDM more recent, alternative models. A key result appearance scale-free behavior fractal dimension, reliably large over many epochs. Finally, appendix gives some details simulation methods these studies.