2018/02/28 by M. Cariglia, A. Galajinsky, G. W. Gibbons +1 · 1 citation
Physics and Astronomy · Mathematics · #gr-qc #astro-ph.CO #hep-th #math-ph #math.MP
paper · pdf · doi:10.1140/epjc/s10052-018-5789-x
Minor corrections and precisions, a couple of references added. 34 pages, 3 figures. To be published in European Physical Journal C
arxiv created 2018/04/10 · arxiv updated 2018/05/09
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.