Conformal and projective symmetries in Newtonian cosmology

Christian Duval (1) , Gary Gibbons (2) , Peter Horvathy (3)

1 CPT - Centre de Physique Théorique - UMR 7332
2 DAMTP - Department of Applied Mathematics and Theoretical Physics
3 LMPT - Laboratoire de Mathématiques et Physique Théorique

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, it contrast with the Schrödinger group or the Conformal Galilei Algebra.

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Physique des Hautes Energies - Théorie [hep-th]; Physique mathématique [math-ph]

Christian Duval, Gary Gibbons, Peter Horvathy. Conformal and projective symmetries in Newtonian cosmology. 2016. ⟨hal-01308770v1⟩