Scaling Behavior for the Susceptibility of the Vacuum

Christopher Pilot

doi:10.4236/ijaa.2021.111002

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., G-1=G-1(a), to form the most general scaling laws for polarization of the vacuum. The positive and negative values for the Planckion mass, which form the basis of the Winterberg model, are inextricably linked to the value of G, and as such, both G and Planck mass are intrinsic properties of the vacuum. Scaling laws for the non-local, smeared, cosmic susceptibility, , the cosmic polarization, , the cosmic macroscopic gravitational field, , and the cosmic gravitational field mass density, , 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, . 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, z=1.66, for susceptibility model I, and, z=2.53 , for susceptibility model II.

Highlights

Cosmic susceptibility, and cosmic polarization are natural consequences of a Hajdukovic/Winterberg model for space
We keep in mind that, = ax0, where, a, is cosmic scale parameter
We have considered the gravitational susceptibility of space assuming that space is made up of a vast assembly of positive and negative mass particles, called Planckions

Summary

Introduction

Cosmic polarization are natural consequences of a Hajdukovic/Winterberg model for space. Using the idea of polarization due to Hajdukovic, and the notion of positive and negative mass Planckions due to Winterberg, the author developed a theory of gravi statics, which can be used to explain the present day density parameters in Friedmanns’ equation He found that, as a consequence, the cosmic susceptibility in the present epoch amounts to, χ0 = 0.842. The net polarization of the vacuum, cosmically, when averaged over the entire universe, was found to equ= al, P0 ε= 0 χ0 g0 2.396 kg m2 , in the present era, as shown in reference [12] In this equation, χ0 , is the cosmic susceptibility, a smeared quantity. The cosmic net macroscopic gravitational field equals, = g0 2.387E−9 m s2 This is another smeared quantity, obtained from Gauss’s law, which holds point for point in the universe, but only if huge distance scales are considered, greater than 100 Mpc in the current era. The above values for, χ0 , and, g0 , above, were imposed upon us in order to make sense of the present-day density parameters in Friedmanns’ equation, within the ΛCDM

Pilot DOI

Summary and Conclusions