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The famous Dirac sea idea can be resurrected if one replaces the concept of positive and negative matter mass with positive and negative energy. Utilizing this concept, the perpetually spatially-flat matter-generating FSC model can be shown to be a realistic Milne “empty universe” model. Furthermore, this may be why
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ct cosmological models like FSC show an excellent statistical fit with the accumulated data of the Supernova Cosmology Project.

Mathematical physicist Paul Dirac is perhaps best known for the Dirac equation in its many forms [

On a parallel track, there is the currently-favored theory that our universe may have started from a zero-energy state and undergone a brief (10^{−32} s) period of “cosmic inflation” in which all matter and antimatter were created. Nevertheless, this nearly instantaneous matter-generating universe theory would appear to violate conservation of energy. This did not escape notice by its inventor, Alan Guth [

Recently, there have been proposed several perpetually matter-generating universe theories [

spatially-flat universe ( ρ 0 = 3 H 0 2 8 π G ) for any theoretical time of observation (o).

Furthermore, the FSC model tightly correlates the current redshifted cosmic microwave background (CMB) temperature of 2.72548 K with a current predicted Hubble parameter value of 66.9 km∙s^{−1}∙Mpc^{−1}. This Hubble parameter value fits within the tight constraints of the 2018 Planck Collaboration [

The relevance of the Dirac sea idea to the FSC model pertains to its perpetual matter generation and its perpetual spatial flatness. As detailed in several 2018 publications [_{h} = ct cosmological models and observations of the Supernova Cosmology Project indicates, the expansion of our universe appears to be coasting at constant velocity [_{h} = ct models have this “coasting at constant velocity” feature. For specifics concerning the basic features of R_{h} = ct models, the reader is encouraged to start with these references. FSC is one such R_{h} = ct model.

The “Dirac sea” idea can be resurrected if one considers a dichotomy of positive and negative energy states popping into and out of existence within the vacuum. If one follows the convention that all units of matter mass-energy are “positive” energy, then one can consider the “holes” in the Dirac sea to be similarly-sized units of “negative” vacuum energy. Furthermore, since the FSC model uses such a sign convention, the negative energy holes in the FSC Dirac sea can now be understood to be units of dark energy exactly offset by the units of matter mass-energy produced in the FSC vacuum. By this perpetually ongoing process, the FSC model accumulates increasingly positive (matter) energy and increasingly negative dark energy of equal magnitude, always summing to zero total energy. In this way, a universe which begins in a zero-energy state maintains perpetual conservation of total (i.e., global) cosmic energy.

The “net zero energy” FSC model can now be contrasted with standard inflationary cosmology, which considers such models to be unrealistic “empty universe” models. The phrase “empty universe” has generally been applied in the past to Milne-type models containing no matter. However, the current R_{h} = ct models contain matter and, as such, are considered to be more realistic than Milne’s original conception. If one looks carefully at the following open source graph [

This “empty” universe line falls exactly where the FSC and other R_{h} = ct models fall. One can also readily see how it is that R_{h} = ct universe models appear to show an excellent statistical fit with SCP observations to date. For additional proof, another open source graph [

The “flat” line is where the perpetually spatially-flat FSC model falls. Once again, one can readily see that the FSC model shows an excellent statistical fit with the accumulated SCP data.

The significance of the use of the FSC model to resurrect the Dirac sea concept (at least in terms of opposite sign cosmic energies) is perhaps best seen in

One can readily see that the magnitude of positive matter mass-energy (visible plus dark matter) of the FSC model scales in exactly the same way as the magnitude of negative dark energy scales. Thus, the “net zero energy” of the universe as a global object is always maintained. In this context, the “net zero energy” FSC model can be thought of as a realistic Milne-type “empty universe” model!

This paper provides a brief look at Dirac’s thought process concerning how the cosmic vacuum might behave if it follows his famous equation. The “Dirac sea”

idea is resurrected in terms of a zero-point energy vacuum in which energy has positive (i.e., matter) and negative (i.e., dark energy) values always summing to zero (i.e., “net zero energy”). As it turns out, the FSC model, by its perpetual matter generation and its perpetual spacetime flatness, can be seen as a realistic Milne-type “empty universe” model. The genius of Paul Dirac and his equation can once again be readily seen when his “Dirac sea” idea for positive and negative matter (an impossibility) is resurrected in terms of positive and negative energy.

This paper is dedicated to Stephen Hawking and Roger Penrose for their groundbreaking work on black holes and their possible application to cosmology. Dr. Tatum sincerely thanks U.V.S. Seshavatharam for his co-authorship of the seminal FSC papers and some of the more recent FSC publications. He also thanks Dr. Rudolph Schild of the Harvard Center for Astrophysics for his past support and encouragement.

The author declares no conflicts of interest regarding the publication of this paper.

Tatum, E.T. (2019) How the Dirac Sea Idea May Apply to a Spatially-Flat Universe Model (A Brief Review). Journal of Modern Physics, 10, 974-979. https://doi.org/10.4236/jmp.2019.108064