2006/01/20 by B. Marcos, Thierry Baertschiger, T. Baertschiger +6 · 3 citations
Physics and Astronomy · #Cosmology and Gravitation Theories #Galaxies: Formation, Evolution, Phenomena #Gamma-ray bursts and supernovae #Lattice (music) #Mathematical physics #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Physics #Quantum mechanics #Spectral line #Statistical physics #astro-ph #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevd.73.103507
published as Phys.Rev. D73 (2006) 103507 · 25 pages, 21 figures
arxiv created 2006/01/20 · openalex publication_date 2006/05/15 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We present a perturbative treatment of the evolution under their mutual self-gravity of particles displaced off an infinite perfect lattice, both for a static space and for a homogeneously expanding space as in cosmological N-body simulations. The treatment, analogous to that of perturbations to a crystal in solid state physics, can be seen as a discrete (i.e. particle) generalization of the perturbative solution in the Lagrangian formalism of a self-gravitating fluid. Working to linear order, we show explicitly that this fluid evolution is recovered in the limit that the initial perturbations are restricted to modes of wavelength much larger than the lattice spacing. The full spectrum of eigenvalues of the simxple cubic lattice contains both oscillatory modes and unstable modes which grow slightly faster than in the fluid limit. A detailed comparison of our perturbative treatment, at linear order, with full numerical simulations is presented, for two very different classes of initial perturbation spectra. We find that the range of validity is similar to that of the perturbative fluid approximation (i.e. up to close to ``shell-crossing''), but that the accuracy in tracing the evolution is superior. The formalism provides a powerful tool to systematically calculate discreteness effects at early times in cosmological N-body simulations.