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, ΩM2≃4ΩbΩΛ, is derived; the actual observed results are compared to this equation (calculated
ΩM = 0.33 vs. observed ΩM = 0.31); the model might explain the origin of dark energy and dark matter of the
evolution of the universe.