Cosmological principle in Newtonian dynamics

Author:

Benisty David12ORCID,Guendelman Eduardo I.123

Affiliation:

1. Physics Department, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel

2. Frankfurt Institute for Advanced Studies (FIAS), Ruth-Moufang-Strasse 1, 60438 Frankfurt am Main, Germany

3. Bahamas Advanced Study Institute and Conferences, 4A Ocean Heights, Hill View Circle, Stella Maris, Long Island, The Bahamas

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.

Funder

COST

Publisher

World Scientific Pub Co Pte Lt

Subject

General Physics and Astronomy,Astronomy and Astrophysics,Nuclear and High Energy Physics

Reference27 articles.

1. Local gravitational physics of the Hubble expansion

2. Torsional Newton–Cartan geometry and the Schrödinger algebra

3. E. L. Schucking, Relativity Theory and Astrophysics, Lectures in Applied Mathematics, Vol. 8 (American Mathematical Society, 1967), pp. 218–236.

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