Algebraic invariant curves in cosmological dynamical systems and exact solutions

Mathematics – Logic

Scientific paper

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Scientific paper

The Einstein field equations for a number of classes of cosmological models have previously been written as polynomial systems of ordinary differential equations. We show that, for restricted parameter values, these equations admit algebraic invariant curves, which, in turn, lead to exact solutions of the field equations. This property explains the recent discovery of a number of exact solutions and is used to produce additional ones.

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