Scaling Behavior for the Susceptibility of the Vacuum

Abstract

Using the two-component superfluid model of Winterberg for space, two models for the susceptibility of the cosmic 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., ΩΩ Ω Ω = . While this is an unconventional assignment, differing from the ΛCDM model, we believe this is correct, as localized dark matter (LDM) contributions can be much higher in this epoch than cosmic smeared values for susceptibility. All density parameter assignments in Friedmanns' equation are cosmic averages, valid for distance scales in excess of 100 Mpc in the current epoch. 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, 1.66 z = , for susceptibility model I, and, 2.53 z = , for susceptibility model II.

Predicting the Curvature of the Cosmos, and Point of Volume Contraction in a Big Bounce Scenario

“…What is needed for our purposes are the scaling laws for dark matter, and dark energy. These were found in reference [18] as, ( . We are adopting a Winterberg model for space, where we have a vast assembly (sea) of positive and negative mass Planck particles, which together form an electrically neutral, and massively neutral medium, the vacuum, in the unperturbed state.…”

“…We will also need a specific mechanism for decreasing the total density parameter in Friedmann's equation. This is done in Section 3, where we introduce a decreasing smeared cosmic susceptibility, ( ) a χ , with increasing scale parameter, which is based on previous published work [17] [18]. We will show explicitly how this feature can cause the universe to eventually contract.…”

“…In reference [18], we assumed that ( ) . Only from that point onwards could solids, liquids, and non-ionized gases form.…”

“…Only from that point onwards could solids, liquids, and non-ionized gases form. We assumed specific functions whereby ( ) a χ increased with increasing cosmic scale parameter in reference, [18]. However, this will never lead to eventual big bounce contraction.…”

“…This is necessary so that, at every point in cosmological time, ( ) ( ) 1 is the relative gravitational permittivity. Equation(3-4a), was an equation that we worked with in reference[18], and assumed an increasing ( ) a χ with increasing cosmic scale parameter, "a". The, λ, in Equation (3-4b), is new, and is a parameter which needs to be determined, if we accept a decreasing ( ) a χ with increasing scale parameter, "a".…”