Noether Symmetry in Newtonian Dynamics and Cosmology

Abstract

The connection between the Cosmological Principle and the Newtonian Dynamics is formulated via Noether Symmetry (NS). [1] formulates the symmetry that connects two different frames with relative acceleration, without an action formulation. Here, this symmetry is derived from a classical particles system that governed by the potential φ. The action with the corresponding symmetry yields a conserved Noether Current (NC). Homogeneous behavior for the coordinate system on the conserved current yields the Friedmann equations.

Hyperbolic space in the Newtonian limit: The cosmological constant

“…One such simplification is provided by the Newtonian limit [2,3,15,17,35,36,37], as opposed to the fully relativisitic regime. Further advantage is provided by the duality between the Newtonian cosmological fluid on the one hand, and the probability fluid of nonrelativistic quantum mechanics, on the other.…”