Computational Cosmology: From the Early Universe to the Large Scale Structure

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.

Spacetime and the Passage of Time

“…Then (31) determines the rate of change of the metric g ij (x α ) relative to the ADM time coordinate; (32) determines the rate of change of the geometric source terms π ij occurring in (31); the matter equations determine the rate of change of the matter terms. How this works out in practice is shown in depth in [4]. Overall this determines the metric tensor as a function of time, and hence evolution of the surfaces of constant time as defined above (which are determined by the metric).…”

“…The specific experimental outcome (17) that will be measured by an observer to occur at a later time is not determined by the Everett hypothesis. 4 Thus the initial state (15) does not uniquely determine the final state (17); and this is not due to lack of data, it is due to the foundational nature of quantum interactions. You can predict the statistics of what is likely to happen but not the unique actual physical outcome, which unfolds in an unpredictable way as time progresses; you can only find out what this outcome is after it has happened.…”

Homogeneous loop quantum cosmology

“…The gravitational field equations, for instance in the case of cosmology where one can assume homogeneity and isotropy, involve components of curvature as well as the inverse metric. (Computational methods to derive information from these equations are described in [72].) Since singularities occur, these components will become large in certain regimes, but the equations have been tested only in small curvature regimes.…”

A novel approach for partitioning iteration spaces with variable densities

“…Such loop nests are commonly found in various applications such as 3-d graphics (mesh collapsing, volume rendering [6], geometric modeling of nonhomogeneous 3-d objects), aircraft simulations, cosmological and N-body simulations [7] et cetera. Without loss of any generality, we assume that the outermost loop is normalized from 1 to N with s1 = 1.…”

“…TSoE identifies all prime 7 A loop is multiway nested if there are two or more loops at the same level [14]. Note that the loops may be nested themselves.…”