Ermakov-Pinney equation in scalar field cosmologies

@article{Hawkins2002ErmakovPinneyEI,
  title={Ermakov-Pinney equation in scalar field cosmologies},
  author={Rachael M. Hawkins and James E. Lidsey},
  journal={Physical Review D},
  year={2002},
  volume={66},
  pages={023523}
}
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… 
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