Table of Contents
Journal of Gravity
Volume 2014 (2014), Article ID 415649, 5 pages
Research Article

Gravitational Lagrangians, Mach’s Principle, and the Equivalence Principle in an Expanding Universe

KTH Mechanics, 100 44 Stockholm, Sweden

Received 13 June 2014; Accepted 6 August 2014; Published 17 August 2014

Academic Editor: Kazuharu Bamba

Copyright © 2014 Hanno Essén. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Gravitational Lagrangians as derived by Fock for the Einstein-Infeld-Hoffmann approach, and by Kennedy assuming only a fourth rank tensor interaction, contain long range interactions. Here we investigate how these affect the local dynamics when integrated over an expanding universe out to the Hubble radius. Taking the cosmic expansion velocity into account in a heuristic manner it is found that these long range interactions imply Mach’s principle, provided the universe has the critical density, and that mass is renormalized. Suitable higher order additions to the Lagrangians make the formalism consistent with the equivalence principle.