Cosmological models expressible as gradient vector fields

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Abstract
Classes of cosmological models, for which Einstein’s equations reduce to two-dimensional dynamical systems, are studied in the presence of stochastic perturbations using the steady state of the associated Fokker–Planck equations and Zeeman’s notion of ε-stability. In all cases, a set of variables is found for which the dynamical systems are expressible as gradient vector flows, showing that the associated cosmologies are stochastically stable. Such models are also important in connection with application of catastrophy theory to cosmology.

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