Phys. Rev. Lett. 95, 011304 (2005) [4 pages]Gravitational Evolution of a Perturbed Lattice and its Fluid LimitReceived 8 April 2005; published 30 June 2005 We apply a simple linearization, well known in solid state physics, to approximate the evolution at early times of cosmological N-body simulations of gravity. In the limit that the initial perturbations, applied to an infinite perfect lattice, are at wavelengths much greater than the lattice spacing l, the evolution is exactly that of a pressureless self-gravitating fluid treated in the analogous (Lagrangian) linearization, with the Zeldovich approximation as a subclass of asymptotic solutions. Our less restricted approximation allows one to trace the evolution of the discrete distribution until the time when particles approach one another (i.e., “shell crossing”). We calculate modifications of the fluid evolution, explicitly dependent on l, i.e., discreteness effects in the N-body simulations. We note that these effects become increasingly important as the initial redshift is increased at fixed l. © 2005 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.95.011304
DOI:
10.1103/PhysRevLett.95.011304
PACS:
98.80.−k, 95.10.Ce
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