Unification of Conformal and Fuzzy Gravities With Internal Interactions Resulting in SO(10) and a Possible Probe Through Stochastic Gravitational Wave Background

Abstract

The unification of conformal and fuzzy gravities with internal interactions is based on the facts that i) the tangent group of a curved manifold and the manifold itself do not necessarily have the same dimensions and ii) both gravitational theories considered here have been formulated in a gauge theoretic way. The gauge-theoretic approach of gravities, commenting in particular on their diffeomorphism invariance, and the construction of conformal and noncommutative (fuzzy) gravity using the gauge-theoretic framework are reviewed. Based on an extension of the four-dimensional tangent group, unification of both gravities with the internal interactions is achieved. Both unified schemes are examined at 1-loop level considering suitable spontaneous symmetry breakings to a $SO\left(10\right)$ grand unified theory and consequently down to the Standard Model of particle physics through four specific spontaneous symmetry breaking channels. Each channel is examined against proton lifetime experimental bounds and its observation potential through gravitational signal from cosmic strings production is discussed.