Cosmological aspects of the Eisenhart-Duval lift
General Relativity and Quantum Cosmology
2018-05-09 v3 Cosmology and Nongalactic Astrophysics
High Energy Physics - Theory
Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.1802.03370,
title = {Cosmological aspects of the Eisenhart-Duval lift},
author = {M. Cariglia and A. Galajinsky and G. W. Gibbons and P. A. Horvathy},
journal= {arXiv preprint arXiv:1802.03370},
year = {2018}
}
Comments
Minor corrections and precisions, a couple of references added. 34 pages, 3 figures. To be published in European Physical Journal C