On (2 + 1)-dimensional Friedmann-Robertson-Walker universes: an Ermakov-Pinney equation approach

In this letter, we examine the reduction of Friedmann-Robertson-Walker-type models in 2 + 1 dimensions, to an ErmakovPinney 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 ʹdataʹ 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.