Any comprehensive model of cosmology must therefore include nonlinear interactions between different matter sources and spacetime curvature. A realistic model of the Universe must also cover large dynamical spatial and time scales, extreme temperature and density distributions, and highly dynamic atomic and molecular matter compositions. In addition, due to all the varied physical processes of cosmological significance, one must draw from many disciplines of physics to model curvature anisotropies, gravitational waves, electromagnetic fields, nucleosynthesis, particle physics, hydrodynamic fluids, etc. These phenomena are described in terms of coupled nonlinear partial differential equations and must be solved numerically for general inhomogeneous spacetimes. The situation appears extremely complex, even with current technological and computational advances. As a result, the codes and numerical methods that have been developed to date are designed to investigate very specific problems with either idealized symmetries or simplifying assumptions regarding the metric behavior, the matter distribution/composition or the interactions among the matter types and spacetime curvature.

It is the purpose of this article to review various published numerical cosmological calculations; from the very early Universe to the present; from the purely geometrical dynamics of the vacuum field to the quark-hadron phase transition and the large scale structure of the Universe. There are two major sections: § 2 where brief summaries of early Universe and fully relativistic cosmological calculations are presented; and § 3 which focuses on structure formation in the post-combination epoch and on testing cosmological models against observations.

Physical and Relativistic Numerical Cosmology
Peter Anninos
http://www.livingreviews.org/lrr-1998-2
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