Abstract
In order to account for the observable Universe, any comprehensive theory or model of cosmology must draw from many disciplines of physics, including gauge theories of strong and weak interactions, the hydrodynamics and microphysics of baryonic matter, electromagnetic fields, and spacetime curvature, for example. Although it is difficult to incorporate all these physical elements into a single complete model of our Universe, advances in computing methods and technologies have contributed significantly towards our understanding of cosmological models, the Universe, and astrophysical processes within them. A sample of numerical calculations addressing specific issues in cosmology are reviewed in this article: from the Big Bang singularity dynamics to the fundamental interactions of gravitational waves; from the quark-hadron phase transition to the large scale structure of the Universe. The emphasis, although not exclusively, is on those calculations designed to test different models of cosmology against the observed Universe.
Highlights
Numerical investigations of cosmological spacetimes can be categorized into two broad classes of calculations, distinguished by their computational goals: 1) geometrical and mathematical principles of cosmological models, and 2) physical and astrophysical cosmology
The standard picture of cosmology assumes that a phase transition occurred at approximately 10−5 seconds after the Big Bang to convert a plasma of free quarks and gluons into hadrons
Important modifications to the Cosmic Microwave Background Radiation (CMBR) spectrum can arise from large scale coherent structures due to the gravitational redshifting of the photons through the Sachs–Wolfe effect, even well after the photons decouple from the matter at redshift z ∼ 103
Summary
Numerical investigations of cosmological spacetimes can be categorized into two broad classes of calculations, distinguished by their computational (or even philosophical) goals: 1) geometrical and mathematical principles of cosmological models, and 2) physical and astrophysical cosmology. 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 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
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