Relativity and Cosmology


The General Relevance of the Modified Cosmological Model

Authors: Jonathan W. Tooker

The modified cosmological model (MCM) has been an active research program since 2009 and here we summarize the highlights while providing background and insights as they demonstrate mathematical merit. The main ``modification'' that underpins this work is to consider the principle of greatest action, not least, but cosmological energy functions do not appear. To accommodate infinite action, we develop a transfinite analytical framework $^\star\mathbb{C}$. In the first chapter, we define the MCM system as the union of two Kaluza--Klein theories disconnected by a topological obstruction. We identify a detail overlooked by Feynman in his ``many double slits'' thought experiment with which we directly motivate the principle of maximum action. Chapter two is mostly a review of fundamental concepts including twistors and quaternions. Much attention in chapter three is given to what are perceived as criticisms of the MCM mechanism for the unification of the theories of gravitation and quanta, and we closely examine the derivation of Einstein's equation from unrelated MCM concepts. The main technical result in chapter three is to demonstrate that dark energy and expanding space are inherent to the MCM metric and we examine the role of the advanced electromagnetic potential in ``hyperspacetime.'' Chapter four is a tour de force starting with a review of the foundations of the MCM. We extend Dirac's bra-ket to an MCM inner product for $^\star\mathbb{C}$. We continue with a study of conformal infinity and the transfinite extension into the region ``beyond conformal infinity.'' The double slit experiment gives an example of the empirical/philosophical utilities of the MCM principles and we examine their extension into the realm of numerical analysis before deriving the main result: a new formulation for the mass-energy budget of the universe that agrees perfectly with $\Lambda$CDM.

Comments: 284 Pages. 96 figures, solid

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Submission history

[v1] 2017-12-25 14:56:26
[v2] 2018-01-04 11:18:29
[v3] 2018-05-21 04:34:22

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