# Cosmological equivalence principle and the weak-field limit - General Relativity and Quantum Cosmology

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Abstract: The strong equivalence principle is extended in application to averageddynamical fields in cosmology to include the role of the average density in thedetermination of inertial frames. The resulting cosmological equivalenceprinciple is applied to the problem of synchronisation of clocks in theobserved universe. Once density perturbations grow to give density contrasts oforder one on scales of tens of megaparsecs, the integrated deceleration of thelocal background regions of voids relative to galaxies must be accounted for inthe relative synchronisation of clocks of ideal observers who measure anisotropic cosmic microwave background. The relative deceleration of thebackground can be expected to represent a scale in which weak-field Newtoniandynamics should be modified to account for dynamical gradients in the Ricciscalar curvature of space. This acceleration scale is estimated using thebest-fit nonlinear bubble model of the universe with backreaction. At redshiftsz < 0.25 the scale is found to coincide with the empirical acceleration scaleof modified Newtonian dynamics. At larger redshifts the scale varies in amanner which is likely to be important for understanding dynamics of galaxyclusters, and structure formation. Although the relative deceleration,typically of order 10^{-10} m-s^2, is small, when integrated over the lifetimeof the universe it amounts to an accumulated relative difference of 38% in therate of average clocks in galaxies as compared to volume-average clocks in theemptiness of voids. A number of foundational aspects of the cosmologicalequivalence principle are also discussed, including its relation to Mach-sprinciple, the Weyl curvature hypothesis and the initial conditions of theuniverse.

Author: ** David L. Wiltshire**

Source: https://arxiv.org/