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07 February 2025
 
  » arxiv » astro-ph/0112139

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The Ermakov-Pinney Equation in Scalar Field Cosmologies
Rachael M. Hawkins ; James E. Lidsey ;
Date 6 Dec 2001
Journal Phys.Rev. D66 (2002) 023523
Subject Astrophysics; Mathematical Physics | astro-ph gr-qc math-ph math.MP
AbstractIt 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.
Source arXiv, astro-ph/0112139
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