Cosmological equivalence principle and the weakfield limit
Abstract
The strong equivalence principle is extended in application to averaged dynamical fields in cosmology to include the role of the average density in the determination of inertial frames. The resulting cosmological equivalence principle is applied to the problem of synchronization of clocks in the observed universe. Once density perturbations grow to give density contrasts of order 1 on scales of tens of megaparsecs, the integrated deceleration of the local background regions of voids relative to galaxies must be accounted for in the relative synchronization of clocks of ideal observers who measure an isotropic cosmic microwave background. The relative deceleration of the background can be expected to represent a scale in which weakfield Newtonian dynamics should be modified to account for dynamical gradients in the Ricci scalar curvature of space. This acceleration scale is estimated using the bestfit nonlinear bubble model of the universe with backreaction. At redshifts z≲0.25 the scale is found to coincide with the empirical acceleration scale of modified Newtonian dynamics. At larger redshifts the scale varies in a manner which is likely to be important for understanding dynamics of galaxy clusters, and structure formation. Although the relative deceleration, typically of order 10^{10}ms^{2}, is small, when integrated over the lifetime of the universe it amounts to an accumulated relative difference of 38% in the rate of average clocks in galaxies as compared to volumeaverage clocks in the emptiness of voids. A number of foundational aspects of the cosmological equivalence principle are also discussed, including its relation to Mach’s principle, the Weyl curvature hypothesis, and the initial conditions of the universe.
 Publication:

Physical Review D
 Pub Date:
 October 2008
 DOI:
 10.1103/PhysRevD.78.084032
 arXiv:
 arXiv:0809.1183
 Bibcode:
 2008PhRvD..78h4032W
 Keywords:

 04.20.Cv;
 95.36.+x;
 98.80.Jk;
 Fundamental problems and general formalism;
 Dark energy;
 Mathematical and relativistic aspects of cosmology;
 General Relativity and Quantum Cosmology;
 Astrophysics;
 High Energy Physics  Theory
 EPrint:
 17 pages, 5 figures