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 (and numerical methods applied to 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
2.1 A brief chronologyWith current observational constraints, the physical state of our Universe, as understood in the context of the standard or Friedman–Lemaıtre–Robertson–Walker (FLRW) model, can be crudely extrapolated back to ∼ 10−43 seconds after the Big Bang, before which the classical description of general relativity is expected to give way to a quantum theory of gravity
In the former, the emphasis is on the geometric framework in which astrophysical processes occur, for example cosmological expansion, topological singularities, geometrodynamics in general, and classification characteristics or invariants of the many models allowed by the theory of general relativity
These results suggest that distinctions between exits to inflation may be manifested in the process of reheating and as a selected spectrum of inhomogeneous perturbations influenced by resonance mechanisms in curvature oscillations
Summary
Fast-track revision to include recent developments. 37 new references have been added. Page 8: Extended discussion to include a more complete chronology. Page 24: Subsubsection added, new references included. Page 25: Completely rewrote and reorganized section, added new references and a more detailed discussion on various anisotropy contributions. Page 34: Added paragraph which discusses relatively new references on model comparisons. Page 46: Added paragraphs, expanded discussion to include mention of a new paper which uses NOCD methods for modeling ideal gases, and which compares artificial viscosity with conserving numerical methods. Page 47: New section added to include the stress tensor for nonideal fluids with shear stress. Page 49: Reorganized section by adding new subsubsection, added example of a typical chemical network useful for primordial cosmology. Page 51: Reorganized section by adding new subsubsection, added reference
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