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In the standard cosmological paradigm the Universe is described by an expanding Friedmann-Robertson-Walker (FRW) model with a hot big bang. Mathematical cosmology involves the study of the early- and late- time behaviour of more general classes of cosmological models as well as the detailed investigation of special exact cosmological solutions with symmetries such as the spatially homogeneous and isotropic models with a Robertson-Walker (RW) geometry and self-similar cosmological models. Dynamical systems techniques are powerful tools in such an investigation. This is particularly true for the qualitative analysis of spatially homogeneous cosmological models whose evolution is governed by a (finite-dimensional) autonomous system of ordinary differential equations (ODE). Inhomogeneous cosmological models can also be studied, but since the evolution equations are autonomous partial differential equations (PDE) in this case the resulting state space is infinite-dimensional (i.e., a function space) , and the analysis is considerably more complicated.
KeywordsCosmological Model Perfect Fluid Ordinary Differential Equation Partial Differential Equation Heteroclinic Cycle
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