The Ermakov-Pinney Equation in Scalar Field Cosmologies

Abstract

It is shown that the dynamics of cosmologies sourced by a mixture of perfect fluids and self-interacting scalar fields are described by the non-linear, Ermakov-Pinney equation. The general solution of this equation can be expressed in terms of particular solutions to a related, linear differential equation. This characteristic is employed to derive exact cosmologies in the inflationary and quintessential scenarios. The relevance of the Ermakov-Pinney equation to the braneworld scenario is discussed.

16 pages, 2 figures, references added, extended discussion emphasising importance of scale factor in derivation

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