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
It is believed that several spontaneous symmetry breaking (SSB) phase transitions transpired in the early Universe as it expanded and cooled, including: the grand unification transition (GUT) at ∼ 10−34 seconds after the Big Bang
This marks an era of inflationary expansion and the origin of matter–antimatter asymmetry through baryon, charge conjugation, and charge + parity violating interactions and nonequilibrium effects.); the electroweak (EW) SSB transition at ∼ 10−11 secs; and the chiral (QCD) symmetry breaking transition at ∼ 10−5 secs during which quarks condensed into hadrons
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 published numerical cosmological calculations addressing issues from the very early Universe to the present; from the purely geometrical dynamics of the initial singularity to the large scale structure of the Universe. There are three major sections: § 2 where a brief overview is presented of various defining events ocurring throughout the history of our Universe and in the context of the standard model; § 3 where brief summaries of early Universe and fully relativistic cosmological calculations are presented; and § 4 which focuses on structure formation in the post-recombination epoch and on testing cosmological models against observations
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