This review is intended to provide
a flavor of the variety of numerical
cosmological calculations performed of different phenomena occurring
throughout the history of our Universe. The topics discussed
range from the strong field dynamical behavior of spacetime geometry
at early times near the Big Bang singularity and the epoch of inflation,
to the late time evolution of large scale
matter fluctuations and the formation of clusters of galaxies.
Although a complete, self-consistent, and accurate description
of our Universe is impractical considering the complex
multiscale and multiphysics requirements, a number of
enlightening results have been demonstrated through computations.
For example, both monotonic AVTD and chaotic oscillatory BLK
behavior have been found in the asymptotic approach to
the initial singularity in a small set of
inhomogeneous Bianchi and Gowdy models,
though it remains to be seen what the generic behavior
might be in more general multidimensional spacetimes.
Numerical calculations suggest that scalar fields
play an important complicated role in the nonlinear or chaotic
evolution of cosmological models with consequences
for the triggering (or not) of inflation and the subsequent
dynamics of structure formation. It is possible, for example, that
these fields can influence the details of inflation and
have observable ramifications as fractal patterns
in the density spectrum, gravitational waves, galaxy distribution,
and cosmic microwave background anisotropies.
All these effects require further studies. Numerical simulations
have been used to place limits on curvature anisotropies
and cosmological parameters
at early times by considering primordial nucleosynthesis
in anisotropic and inhomogeneous cosmologies.
Finally, the large collection of calculations performed of the
post-recombination epoch (for example, cosmic microwave,
gravitational lensing, Lyman-alpha absorption, and galaxy cluster
simulations) have placed strong constraints
on the standard model parameters and structure formation
scenarios when compared to observations. Considering the range of
models consistent with inflation, the preponderance of
observational, theoretical and computational data suggest a best fit
model that is spatially flat with a cosmological constant
and a small tilt in the power spectrum.
Obviously many fundamental issues remain unresolved, including
the background or topology of the cosmological model which best
describes our Universe, the generic singularity behavior,
the dynamics of inflaton fields, the imprint of complex
interacting scalar fields, the fundamental nonlinear curvature
and gravitational wave interactions,
the correct structure formation scenario,
and the origin and spectrum of primordial fluctuations, for example,
are uncertain. However the field of numerical cosmology has
matured in the development of computational techniques, the modeling
of microphysics, and in taking advantage of current computing
technologies, to the point that it is now possible to perform
high resolution multiphysics simulations and
reliable comparisons of numerical models with observed data.
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Computational Cosmology: from the Early Universe to the Large Scale Structure
Peter Anninos
http://www.livingreviews.org/lrr-2001-2
© Max-Planck-Gesellschaft. ISSN 1433-8351
Problems/Comments to livrev@aei-potsdam.mpg.de
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