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Cosmological aspects of the Eisenhart–Duval lift

M. Cariglia A. Galajinsky G.W. Gibbons P.A. Horvathy 1
1 IDP - Institut Denis Poisson
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.
Keywords : rotation Killing geodesic space-time isometry Friedman model translation tensor: energy-momentum cosmological model
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https://hal.archives-ouvertes.fr/hal-01719548
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Submitted on : Wednesday, February 28, 2018 - 11:55:04 AM
Last modification on : Wednesday, May 12, 2021 - 2:10:15 AM

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M. Cariglia, A. Galajinsky, G.W. Gibbons, P.A. Horvathy. Cosmological aspects of the Eisenhart–Duval lift. Eur.Phys.J.C, 2018, 78 (4), pp.314. ⟨10.1140/epjc/s10052-018-5789-x⟩. ⟨hal-01719548⟩

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