Noether symmetry in Newtonian dynamics and cosmology

A new symmetry for Newtonian Dynamics is analyzed, this corresponds to going an accelerated frame, which introduces a constant gravitational field into the system and subsequently. We consider addition of linear contribution potential $$\phi $$ can be used cancel induced by from, combination these two operations produces then symmetry. This leads Noether current conserved. The conserved charges are analyzed in special cases. may not if flux at infinity, but such eliminated CM (center mass) case isolated system. In frame charge vanishes, Then we study connection between Cosmological Principle was formulated via (Benisty Guendelman Mod Phys Lett 35:2050131, 2020) type, without action formulation. Homogeneous behavior coordinate relevant cosmology zero requirement invariant under yields Friedmann equations, appear as consistency condition