F L Williams and P G Kevrekidis 2003 Class. Quantum Grav. 20 L177 doi:10.1088/0264-9381/20/13/101
F L Williams and P G Kevrekidis
Show affiliationsIn this letter, we examine the reduction of Friedmann–Robertson–Walker-type models in 2 + 1 dimensions, to an Ermakov–Pinney equation. The procedure is used to derive previously known solutions for some specific cosmological models. It is also examined as an inverse problem, wherein the scale factor of the metric or the scalar field coupled to it are postulated and the remaining 'data' of the problem (such as e.g., the scalar field potential) are reconstructed systematically via the Ermakov–Pinney approach. This alternative approach allows us to construct novel solutions for a number of different scalar potentials.
Issue 13 (7 July 2003)
Received 14 April 2003
Published 10 June 2003
F L Williams and P G Kevrekidis 2003 Class. Quantum Grav. 20 L177
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