Cosmological Principle in Newtonian Dynamics
  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 NSL (Newton's Second
Law) or the Poisson equation. For example by replacing NSL with non-linear
function of the acceleration the concept of relative acceleration is lost and
the homogeneity of the universe breaks.
