Scaling Behavior for the Susceptibility of the Vacuum

Abstract

Based on a model of Winterberg, where the vacuum is made up of a two component, positive and negative mass superfluid/ supersolid, we derive scaling laws for the polarization of space, i.e., the vacuum. Upon expansion of the universe, this vast assembly (sea) of positive, and negative mass planckions form a rigid, ether-like, medium, which at sufficiently low temperatures, can be polarized through gravitational alignment/ ordering of planckion mass dipoles. Two models for susceptibility of the vacuum as a function of the cosmic scale parameter, a , are presented. We also consider the possibility that Newton’s constant can scale, i.e., G^(-1)=G^(-1) (a), to form the most general scaling laws for polarization of the vacuum. The positive and negative mass of the planckion, is inextricably related to the value of, G, and as such, both are intrinsic properties of the vacuum. Scaling laws for the non-local, cosmic susceptibility, χ (a), the cosmic polarization, P (a), the cosmic macroscopic gravitational field, g (a), and the cosmic gravitational field mass density, (ρ_gg ) (a), are worked out, with specific examples. At the end of recombination, i.e., the era of last scattering, using the polarization to explain dark matter, and the gravitational field mass density to explain dark energy, we find that, (Ω_(rad,1) ,〖 Ω〗_(b,1 ),Ω_(c,1),Ω_(Λ,1))=(.37,.19,0,.44). While this is an unconventional assignment, differing from the ΛCDM model, we believe this is correct, and we give our reasons why. Among them is the fact that localized dark matter (LDM) contributions can be much higher in this epoch than smeared values for susceptibility. The above assignments are cosmic averages, and will not apply locally. We also evaluate the transition from ordinary matter dominance, to dark matter dominance, for the cosmos as a whole. We obtain for the transition points, z=1.66, for susceptibility model I, and, z=2.53, for susceptibility model II.