Conformal and projective symmetries in Newtonian cosmology

Abstract : Definitions of non-relativistic conformal transformations are considered both in the Newton-Cartan and in the Kaluza-Klein-type Eisenhart/Bargmann geometrical frameworks. The symmetry groups that come into play are exemplified by the cosmological, and also the Newton-Hooke solutions of Newton's gravitational field equations. It is shown, in particular, that the maximal symmetry group of the standard cosmological model is isomorphic to the 13-dimensional conformal-Newton-Cartan group whose conformal-Bargmann extension is explicitly worked out. Attention is drawn to the appearance of independent space and time dilations, in contrast with the Schr{\"o}dinger group or the Conformal Galilei Algebra.
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Christian Duval, G.W. Gibbons, P.A. Horváthy. Conformal and projective symmetries in Newtonian cosmology. Journal of Geometry and Physics, Elsevier, 2017, 112, pp.197--209. ⟨10.1016/j.geomphys.2016.11.012⟩. ⟨hal-01308770v3⟩

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