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15 February 2025
 
  » arxiv » 1605.0231

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Conformal and projective symmetries in Newtonian cosmology
Christian Duval ; Gary Gibbons ; Peter Horvathy ;
Date 1 May 2016
AbstractDefinitions 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, it contrast with the Schr{"o}dinger group or the Conformal Galilei Algebra.
Source arXiv, 1605.0231
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