Unification of Conformal and Fuzzy Gravities with Internal Interactions - study of their behaviour in low energies and possible signals in the detection of Gravitational Waves

Abstract

The Unification of Conformal and Fuzzy gravities with Internal Interactions is based on the following two facts. The first is that the tangent group of a curved manifold and the manifold itself do not necessarily have the same dimensions. The second is that both gravitational theories considered here have been formulated in a gauge theoretic way. Here we would like to start by reviewing the gauge theoretic approach of gravities commenting in particular their diffeomorphism invariance. Then we will review the construction of the Conformal Gravity and the Noncommutative (Fuzzy) Gravity using the gauge theoretic framework. Finally based on an extension of the four-dimensional tangent group we will present the Unification of both Gravities with the Internal Interactions. Both unified schemes will be examined further concerning their behaviour in low energies after suitable spontaneous symmetry breakings as well as the possible signals of the related cosmic strings in the gravitational waves.