$SU(\infty)$-QGR: Emergence of Gravity in an Infinitely Divisible Quantum Universe

Abstract

SU p8q-QGR is a foundationally quantum approach to gravity. It assumes that Hilbert spaces of the Universe as a whole and its subsystems represent the symmetry group SU p8q. The Universe is divided to infinite number of subsystems based on an arbitrary finite rank symmetry group G, which arises due to quantum fluctuations and clustering of states. After selection of two arbitrary subsystems as clock and reference observer, subsystems acquire a relative dynamics, and gravity emerges as a SU p8q Yang-Mills quantum field theory, defined on the (3+1)-dimensional parameter space of Hilbert spaces of the subsystems. As a Yang-Mills model SU p8q-QGR is renormalizable and despite prediction of a spin-1 field for gravity at quantum level, when QGR effects are not detectable, it is perceived similar to Einstein gravity. The aim of the present work is to make the foundation of SU p8q-QGR more mathematically rigorous and fill the gaps in the construction of the model reported in earlier works. In particular, we show that the global SU p8q symmetry manifests itself through the entanglement of every subsystem with the rest of the Universe. Moreover, we demonstrate irrelevance of the geometry of parameter space, which can be gauged out by a SU p8q gauge transformation up to an irrelevant constant. Therefore, SU p8q-QGR deviates from gauge-gravity duality models, because the perceived classical spacetime is neither quantized, nor considered to be non-commutative. In fact, using quantum uncertainty relations, we demonstrate that the classical spacetime and its perceived geometry present the average path of the ensemble of quantum states of subsystems in their parameter space. Thus, SU p8q-QGR explains both the dimension and signature of the classical spacetime. We also briefly discuss SU p8q-QGR specific models for dark energy.