Abstract

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.

Highlights

  • We looked for the simplest mathematical object to identify the underlying reality of nature, and we found it to be cross-ratio

  • We formulate an alternative theory of the dynamics of curvature of spacetime to recover the spinor general relativity equivalent counterpart

  • The complete correspondence between cross-ratio deformation and isomonodromic integratable system used in this article is not yet covered

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Summary

INTRODUCTION

We looked for the simplest mathematical object to identify the underlying reality of nature, and we found it to be cross-ratio. Cassidy’s work consists of introducing a 2 by 2 matrix differential equation and related isomonodromic integratable system, so it can describe the deformation. By such machinery, we formulate an alternative theory of the dynamics of curvature of spacetime to recover the spinor general relativity equivalent counterpart (for which a brief introduction is given in “Brief overview of spinor formulation of general relativity” section). Liu.: A quantum theory of spacetime correspondence between tensors and spinors is obtained by the use of a hybrid spinor σνCD′ (2 Â 2 Hermitian matrix per CD index, denoted as σν in short) (Einstein’s summation notation is used in this article): rlAC0 rn BC0 þ rn

A C0 rl BC0
A AB D ð32Þ
DISCUSSION
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