Conformal and projective symmetries in Newtonian cosmology
  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. 
C. Duval (CPT), G.W. Gibbons (DAMTP/CMS), P.A. Horv\'athy (LMPT)
gr-qc hep-th math-ph math.MP