# Cosmological Principle in Newtonian Dynamics

## TL;DR

This paper explores how the cosmological principle relates to Newtonian dynamics, showing that certain symmetries and the Friedmann equations depend on the form of Newton's laws and gravitational potential.

## Contribution

It demonstrates the connection between the equivalence principle, universe homogeneity, and Newtonian gravity, deriving Friedmann equations from symmetry considerations.

## Key findings

- Friedmann equations emerge from invariance conditions in Newtonian cosmology.
- Modifications to Newton's Second Law or Poisson equation break homogeneity.
- Symmetries are crucial for the consistency of Newtonian cosmological models.

## 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 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.