English

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