http://arxiv.org/abs/1802.03370
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.
M. Cariglia, A. Galajinsky, G. Gibbons, et. al.
Mon, 12 Feb 18
30/53
Comments: 32 pages, 3 figures