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# A quantum theory of spacetime in spinor formalism and the physical reality of cross-ratio representation: the equation of density parameters of dark energy, matter, and ordinary matter is derived: ΩM2 = 4 Ωb ΩΛ

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### ABSTRACT

By theorizing the physical reality through the deformation of an arbitrary cross-ratio, we leverage Galois differential theory to describe the dynamics of isomonodromic integratable system. We found a new description of curvature of spacetime by the equivalency of isomonodromic integratable system and Penrose’s spinor formalism of general relativity. Using such description, we hypothetically quantize the curvature of spacetime (gravity) and apply to the problem of the evolution of the universe. The Friedmann equation is recovered and compared so that the mathematical relationship among dark energy, matter (dark matter + ordinary matter), and ordinary matter, $Ω M 2 ≃ 4 Ω b Ω Λ$ , is derived; the actual observed results are compared to this equation (calculated Ω M = 0.33 vs. observed Ω M = 0.31); the model might explain the origin of dark energy and dark matter of the evolution of the universe.

### Most cited references9

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### Spinors A Mathematica package for doing spinor calculus in General Relativity

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### An introduction to modern astrophysics

(2007)
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### Chapters 13 of A spinor approach to general relativity

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### Author and article information

###### Affiliations
Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA, USA
###### Author notes
[* ]Corresponding author’s e-mail address: jackieliu0@ 123456gmail.com
###### Contributors
(View ORCID Profile)
###### Journal
SOR-PHYS
ScienceOpen Research
ScienceOpen
2199-1006
27 August 2016
25 September 2016
: 0 (ID: 27ffb33f-f6eb-4638-8316-9f74d68ebae1 )
: 0
: 1-11
3802:XE
10.14293/S2199-1006.1.SOR-PHYS.A4HPPH.v1
© 2016 J. C. H. Liu

This work has been published open access under Creative Commons Attribution License CC BY 4.0 , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com .

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Figures: 0, Tables: 0, References: 6, Pages: 11
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