Inertia in Friedmann Universes with variable G $G$ and Λ $\varLambda$

Abstract

In light of the recent interest in dynamical dark energy models based on a cosmology with varying gravitational and cosmological parameters G and Λ, we present here a model of inertia in a type of Friedmann universe with G = G 0 (A/A 0 ) σ ; A being the dimensionless scale factor, that was recently studied by Singh et al. (Astrophys. Space Sci. 345:213, 2013). The proposed Machian model of inertia utilizes the curved space generalization of Sciama's law of inertial induction, which is based on the analogy between the retarded far fields of electrodynamics and those of gravitation, and expresses the total inertial force F = −ma on an accelerating mass m in terms of contributions from all matter in the observable Universe. We show that for a varying Friedmann model with σ = −3/2, inertial induction alone can account for the total inertial force on the accelerating mass. We then compare this cosmological model with current observational constraints for the variation of G.