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arXiv · 1802.03370

Cosmological aspects of the Eisenhart-Duval lift

M. Cariglia·A. Galajinsky·G. W. Gibbons·P. A. Horvathy
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Abstract

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 the Ermakov-Milne-Pinney equation. Killing isometries include spatial translations and rotations, Newton--Hooke boosts and translation in the null direction. Geodesic motion in Ermakov-Milne-Pinney cosmoi is analyzed. The derivation of the Ermakov-Lewis invariant, the Friedmann equations and the Dmitriev-Zel'dovich equations within the Eisenhart--Duval framework is presented.

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M. Cariglia, A. Galajinsky, G. W. Gibbons, P. A. Horvathy. 2018-04-10. Cosmological aspects of the Eisenhart-Duval lift. https://doi.org/10.1140/epjc%2Fs10052-018-5789-x

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