Conjuncted: Sheaf Cohomology as the Mathematical Tool Necessary to Describe a Conformally Invariant Isomorphism. Twistors and Spinors Theoreticals. Note Quote.

Via Cosmological Framework.

The characterization of gravitational forces is nothing but the effect on matter and energy of a modification of the geometry of space-time. This major property of General Relativity remains unchanged. The main difference concerns the dynamics that this geometry obeys. In GTR the dynamics of the gravitational field depends on the curvature invariants; in the Spinor Theory of Gravity such a specific dynamics simply does not exist: the geometry evolves in space-time according to the dynamics of the spinors. The metric is not a field of its own, it does not have an independent reality but is just a consequence of the universal coupling of matter with the fundamental spinors. The motivation of walking down only half of Einstein’s path to General Relativity is to avoid certain known problems that still plague this theory, including its difficult passage to the quantum world and the questions put into evidence by astrophysics involving many discoveries such as the acceleration of the universe, the problems requiring dark matter and dark energy. It seems worthwhile to quote Dark Energy Task Force here :

Dark energy appears to be the dominant component of the physical Universe, yet there is no persuasive theoretical explanation for its existence or magnitude. The acceleration of the Universe is, along with dark matter, the observed phenomenon that most directly demonstrates that our theories of fundamental particles and gravity are either incorrect or incomplete. Recent observations in Cosmology are responsible for an unexpected attitude: to take seriously the possibility of alterating Einstein’ s theory of gravity.

The Spinorial Theory of Gravity presents the possibility of a way out of these difficulties. The reason, which will be explained later on, can be understood from the fact that in the STG there is no direct relationship between the acceleration of the scale factor of the universe and the matter/energy distribution, contrary to the case of GTR, in which the Friedman equation that controls the dynamics of the universe relates the matter-energy content to the geometry through the evolution of the scale factor a(t): ä/a = -1/6 (ρ + 3ρ)

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