The Ermakov-Pinney Equation in Scalar Field Cosmologies
Astrophysics
2009-11-07 v2 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.astro-ph/0112139,
title = {The Ermakov-Pinney Equation in Scalar Field Cosmologies},
author = {Rachael M. Hawkins and James E. Lidsey},
journal= {arXiv preprint arXiv:astro-ph/0112139},
year = {2009}
}
Comments
16 pages, 2 figures, references added, extended discussion emphasising importance of scale factor in derivation