Cosmological principle in Newtonian dynamics

Abstract

A correspondence between the equivalence principle and the homogeneity of the universe is discussed. In Newtonian gravity, translation of co-moving coordinates in a uniformly expanding universe defines an accelerated frame. A consistency condition for the invariance of this transformation which requires a well-defined transformation for the Newtonian potential, yields the Friedmann equations. All these symmetries are lost when we modify Newton’s Second Law (NSL) or the Poisson equation. For example, by replacing NSL with nonlinear function of the acceleration, the concept of relative acceleration is lost and the homogeneity of the universe breaks.