Quantum cosmology


The visible baryonic matter is rare.

Science is a permanent reiteration of (i) observations and experimentations, (ii) data analyzes and models building, (iii) examinations of the adequation between the consequences of these models and the experimental reality, now and in the future.  

A cosmology is a specific scenario describing the history of our universe. The provisory consensus is based on the Einstein’ theory of relativity and called the LambdaCDM cosmological standard model; its belief: all what can be observed today is the late consequence of an initial Big-Bang.

It does not explain the flatness of the universe, its absence of horizon and the origin of the primordial fluctuations able to justify the birth of galaxies [01; Introduction]. In that extent, it fails at level (iii) of the usual scientific methodology.

Since no model should be regarded as a definitive set of dogma, the rationalistic attitude commands to start the play again at level (i) and (ii). Although previous observations have taught us to consider direct sensitive observations (eyes, hears, …) in a very precautious way, the first impressions suggesting the rarity of visible matter are now confirmed by numerous sophisticated measurements [02; WBaryonic ~ 2%]. This is the fact that the theory of the (E) question (short: TEQ; technically: theory of deformed tensor products) will promote as its first axiom.

Fluctuations between diverse forms of the energy are plausible.

If it is believed that, like in classical physics or like in thermodynamics, the energy is a universal concept presenting multiple visages (polymorphism) and that any set of visages is able to transform into another one in adequate procedures depending on concrete circumstances, then a new cosmological scenario may arise from the same actual set of observations. The visible matter is the top of an energetic iceberg, the bottom of which is rooted into a dark ocean.

Deepening that way of thinking, the dark energy sector must be considered as the most stable configuration because it is de facto the most probable too.

With that vision, following generic considerations similar to the ones which are exposed in [01; Introduction], huge regions of our universe should be described by an ad hoc oscillatory wave function and the energy carried by this wave should correspond to the dark one.

I have suggested through an heuristic scenario describing a supra-conducting wave, in [a], that the ad hoc function associated with our supra-conducting four-dimensional universe might be conveniently represented in M(4, R) by the most trivial decomposition of the gravitational term appearing in the covariant expression of the Lorentz force density.

This suggestion contains implicit information on the nature of these dark regions. The matrix itself describes an interaction between a Levi-Civita’ (also called Christoffel’) connection and a four-dimensional phase space.

I am encouraged to go further into that direction because of a technical detail exposed in [01; p. 19, (5.7)].

In opposition with [01], the global scenario of the TEQ does not want to refer to an initial singularity. That choice is rooted in diverse arguments: philosophical, since I see no reason to eliminate the permanent creation-annihilation hypothesis; scientific, since the LCDM does not explain a lot of facts (see first § and e.g.: [03]) and since there exist alternative theories (e.g.: the Loop Quantum Gravity [04] and its Big Bounce [05]) privileging a different vision.

Despite of this fundamental difference, introducing the covariant expression of the Lorentz force density as starting point for a theoretical discussion is seemingly compatible with the quest for a reasonable theory of quantum cosmology.

Some consequences.

Accepting to work with that force as premise allows the discovery of a lot of interesting results. First, involving the extrinsic method, it can be relatively easily proved that, by approximation:

F(up, down) = Φ -  1/2. G-1. Hessf(u)

  • Any (up, down) tensorial representation of the EM-field is in some way centred on the most trivial decomposition of the gravitational term. That representation is compatible with invariant connections and four-speeds.
  • This formalism, alone, suggests also that that representation vanishes in any region of our universe where the inverse four-dimensional metric can be diagonalized.
  • When the function f(u) is a continuous one, there is a specific covariant formulation of the EM-field:


F = 1/2.(G. Φ -  Φt. Gt). 

  • Analysing this formulation with the spirit of E. Cartan’ work on spinors [06], the existence of very peculiar circumstances such that (see [b]):


F = δG 

can be proved. With different words, some EM-fields are equivalent to infinitesimal antisymmetric variations of the four-dimensional metric. These circumstances should be incorporated into the Einstein-Cartan-Sciama-Kibble theory of gravity [07]. An open conceptual question asks if (the, some, all) particles are the representations of these circumstances.

And quite more...


[01] Introductory lectures on quantum cosmology; arXiv:0909.2566v1 [gr-qc], 14 September 2009.

[02] Resolving the H0 tension with diffusion; arXiv:2001.07536v2 [astro-ph.CO], 19 February 2020.

[03] Hubble trouble: a rapidly expanding cosmic debate; physics world, astronomy and space, video, 22 July 2020.

[04] Introduction to loop quantum gravity and to spin foams; arXiv:gr-qc/0409061v3, 9 February 2005.

[05] Alleviating the tension in the CMB using Planck scale physics; Phys. Rev. Lett. 125, 051302, published 29 July 2020.

[06] Cartan, E.: The theory of spinors.

[07] Non-singular, Big-bounce cosmology from spinor torsion coupling; arXiv:1111.4595v2 [gr-qc], 4 July 2012.

Personal contribution:

[a] ISBN I978-2-36923-049-6, v4, 2 July 2020.

[b] ISBN 978-2-36923-085-4.

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event Date de dernière mise à jour : 09/09/2020