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The Universe at the End of Time

Modern cosmology studies the large-scale structure, origin and evolution, and the ultimate fate of the universe as a whole. It attempts to answer crucial questions such as how large and how old the universe is, what geometry it has, and what will happen to it in the future, etc. But these questions are not necessarily independent. For example, what geometry the universe has is key to understand what will happen to it in the future, i.e., whether there will be an eventual contraction and collapse in the form of a big crunch, or whether it will expand forever. In this project, the student will derive the equations that describe the expansion equations for the universe from basic Newtonian physics and, after realizing that analytic solutions are hard to come by, solve these equations numerically assuming open, flat and closed spacetime geometries. To study the far-future behaviour of these solutions, actual cosmological data from existing observational probes will be utilized as initial conditions. The solutions will, it is hoped, shed some light on whether the current expansion of the universe will reverse into a contraction (and possibly resulting in a big crunch, followed by another big bang, maybe?) or whether the expansion continues ad infinitum (but resulting in what possible scenarios?)
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