Cosmology in one dimension: Vlasov dynamics

Abstract

Numerical simulations of self-gravitating systems are generally based on N-body codes, which solve the equations of motion of a large number of interacting particles. This approach suffers from poor statistical sampling in regions of low density. In contrast, Vlasov codes, by meshing the entire phase space, can reach higher accuracy irrespective of the density. Here, we perform one-dimensional Vlasov simulations of a long-standing cosmological problem, namely, the fractal properties of an expanding Einstein-de Sitter universe in Newtonian gravity. The N-body results are confirmed for high-density regions and extended to regions of low matter density, where the N-body approach usually fails.

Structure formation in a Dirac-Milne universe: Comparison with the standard cosmological model

“…Let us now consider an expanding distribution of matter with spherical symmetry. In this case, the gravitational field has only one component E r ðr; tÞ, which depends on time and on a single spatial variable r. This type of system was studied extensively in the past [18][19][20][21][22][23][24][25][26].…”

Structure formation in a Dirac-Milne universe: comparison with the standard cosmological model

“…Let us now consider an expanding distribution of matter with spherical symmetry. In this case, the gravitational field has only one component E r (r, t), which depends on time and on a single spatial variable r. This type of system was studied extensively in the past [18][19][20][21][22][23][24][25][26].…”

Continuous Wavelet Analysis of Matter Clustering Using the Gaussian-derived Wavelet

“…Moreover, the cosmic baryonic density distribution at late times is similar to a fully developed turbulence (Shandarin & Zel'dovich 1989;He et al 2006), which enlightens us to apply these tools to the context of the structure formation of the universe. To illustrate our approach in a more intuitive way, we shall use the 1D matter distributions, since a great deal of work on the largescale structure of the universe is accomplished using 1D cosmology models (Gouda & Nakamura 1989;Fujiwara & Soda 1996;Tatekawa & Maeda 2001;Miller & Rouet 2010;Manfredi et al 2016). The Zel'dovich approximation is a simple model that provides a good approximated solution for the nonlinear evolution of collisionless matter (Zel'dovich 1970).…”