On the graded extension of Thomas-Whitehead projective gravity

Einstein’s theory of general relativity is an exceptional physical theory. Its experimental jury includes the perihelion of Mercury, gravitational lensing, black holes, and gravitational waves. However, there are gravitational phenomena that are not well understood: dark matter, dark energy, and a quantum theory of gravity. The theory of Thomas-Whitehead projective gravity, TWPG is a generalization of Einstein’s framework, which might have a say in this matter. The origins of TWPG lie in the interplay between geodesics, the generalization of straight lines to a curved setting, and projective symmetry, the mathematics capturing the lack of preferred parametrizations carried by geodesics. Furthermore, this formalism introduces a new particle called the Diffeomorphism field.

In this thesis, we further generalize TWPG by lifting the theory to the mathematical set-ting needed to install supersymmetry, SUSY. SUSY is the mathematical blurring of lines that distinguish the two fundamental classes of particles called fermions (electron, neutrino, quark) and bosons (photon, Higgs boson). This mathematical infrastructure can resolve many issues in another outstanding physical theory called the Standard Model of particle physics. The Standard Model accounts for three (electromagnetism, weak, strong) of the four fundamental forces and houses the most accurately (one part in a billion) verified physical prediction. However, the Standard Model is plagued by certain issues such as a lack of understanding of why there is a huge discrepancy between the strength of the weak force and the gravitational force. Introducing the Diffeomorphism field to the Standard Model cast of fundamental particles might resolve some of these problems.