# 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…

## 11 Citations

A non-linear Schrodinger type formulation of FLRW scalar field cosmology

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We show that the Friedmann-Lemaitre-Robertson-Walker equations with scalar field and perfect fluid matter source are equivalent to a suitable non-linear Schrodinger type equation. This provides for…

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Braneworld cosmology for a domain wall embedded in the charged (Anti)-de Sitter-Schwarzschildblack hole of the five--dimensional Einstein-Gauss-Bonnet-Maxwell theory is considered. The effective…

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We report a method of solving for canonical scalar field exact solution in a non-flat FLRW universe with barotropic fluid using non-linear Schrödinger (NLS)-type formulation in comparison to the…

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A cosmological extension of the Eisenhart–Duval metric is constructed by incorporating a cosmic scale factor and the energy-momentum tensor into the scheme. The dynamics of the spacetime is governed…

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Methods for obtaining exact solutions of the dynamical equations in Friedmann–Robertson–Walker spacetime for cosmological models with a scalar field and matter fields or nonzero curvature are…

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The scalar field degree of freedom in Einstein’s plus matter field equations is decoupled for Bianchi type I and V general cosmological models. The source, apart from the minimally coupled scalar…

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We propose a new representation of the Schrödinger-like equation for scalar field Friedmann cosmology where the scalar field is the argument, and the Hubble parameter is the analogue to the wave…

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Elliptic functions are known to appear in many problems, applied and theoretical. However, a lesser known application is in the study of exact solutions to Einstein's gravitational field equations in…