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 by 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.

Original languageEnglish
Article number314
JournalEuropean Physical Journal C
Volume78
Issue number4
DOIs
Publication statusPublished - 1 Apr 2018

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ASJC Scopus subject areas

  • Engineering (miscellaneous)
  • Physics and Astronomy (miscellaneous)

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