Cosmological aspects of the Eisenhart-Duval lift
M. Cariglia, A. Galajinsky, G.W. Gibbons, P.A. Horvathy
TL;DR
This paper extends the Eisenhart-Duval metric to cosmology by incorporating a scale factor and energy-momentum tensor, analyzing spacetime dynamics and geodesics through the Ermakov-Milne-Pinney equation.
Contribution
It introduces a cosmological Eisenhart-Duval metric with new symmetries and derives key equations like Friedmann and Dmitriev-Zel'dovich within this framework.
Findings
Derived the Ermakov-Lewis invariant in this context
Connected the framework to Friedmann equations
Analyzed geodesic motion in cosmological Eisenhart-Duval spacetime
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.
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