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

TL;DR

The paper develops a gauge-theoretic unification of conformal gravity (CG) and noncommutative (fuzzy) gravity (FG) by promoting gravity to a larger tangent-group gauge theory and then further unifying with internal interactions via an $SO(2,16)$ framework. CG arises from gauging the conformal group $SO(2,4)$ and can yield either the Weyl action or Einstein–Hilbert gravity through spontaneous symmetry breaking, while FG is formulated on noncommutative spaces using covariant coordinates and an extended gauge structure that reduces to Palatini gravity in the commutative limit. The unification with internal interactions proceeds through centralizers and staged symmetry breaking starting from an $SO(18)$ (or equivalently $SO(2,16)$) structure down to $SO(10)$ and then to the Standard Model, with a four-family fermion scenario and detailed field-content bookkeeping via intermediate scales: a GUT scale around $M_{GUT} o 10^{15}-10^{16}$ GeV and an intermediate scale $M_I o 10^{10}-10^{13}$ GeV. The phenomenological implications include constraints from proton decay and potential gravitational-wave signals from cosmic strings, offering experimental avenues to probe the high-energy unification, while acknowledging theoretical questions about renormalizability and ghost degrees of freedom that warrant further study.

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.