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 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.

A letter. 4 pages. Minor modifications

References in corpus (7)

• Bimetric MOND gravity
• Mimetic dark matter, ghost instability and a mimetic tensor-vector-scalar gravity
• Field equations and cosmology for a class of nonlocal metric models of MOND
• Origin of the Local Group satellite planes
• Unified Dark Energy and Dark Matter from Dynamical Space Time
• Local gravitational physics of the Hubble expansion
• Global versus Local -- Mach's Principle versus the Equivalence Principle

Cited by in corpus (6)

• The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics
• The Two Body Problem in the Presence of Dark Energy and Modified Gravity: Application to the Local Group
• The Local Group as a test system for Modified Newtonian Dynamics
• Spherical space in the Newtonian limit: The cosmological constant
• Hyperbolic space in the Newtonian limit: the cosmological constant
• Noether Symmetry in Newtonian Dynamics and Cosmology