6 Appendix: Basic Equations and Computational Cosmology: from the Early 4.6 Cosmological sheets

5 Conclusion 

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.



6 Appendix: Basic Equations and Computational Cosmology: from the Early 4.6 Cosmological sheets

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
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