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

• URL: http://arxiv.org/abs/2301.02813v4
• Date: Thu, 4 Jul 2024 18:19:28 GMT
• Title: \boldmath $SU(\infty)$ Quantum Gravity: Emergence of Gravity in an Infinitely Divisible Quantum Universe
• Authors: Houri Ziaeepour,
• Abstract summary: $SU(infty)$-QGR is a foundationally quantum approach to gravity. It assumes that the Hilbert space of the Universe as a whole represents the symmetry group $SU(infty)$. We show that the global $SU(infty)$ symmetry manifests itself through the entanglement of subsystems with the rest of the Universe.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: $SU(\infty)$-QGR is a foundationally quantum approach to gravity. It assumes that the Hilbert space of the Universe as a whole represents the symmetry group $SU(\infty)$, and demonstrates this symmetry for Hilbert spaces of infinite number of subsystems that randomly emerge and represent arbitrary finite rank internal symmetries. It is shown that their states depend on a dimensionful parameter arising due to the breaking of a global $U(1)$ symmetry, and a relative dynamics can be defined by selection of a subsystem as clock. The action has the form of a Yang-Mills quantum field theory defined on the (3+1)-dimensional parameter space for both $SU(\infty)$ - gravity - and internal symmetries. Therefore, $SU(\infty)$-QGR is renormalizable, but predicts a spin-1 mediator for quantum gravity. Nonetheless, it is proved that when quantum gravity effects are not detectable, dynamics is similar to the Einstein-Hilbert action. The aim of present work is in depth study of the foundation and properties of this model. In particular, we show that the global $SU(\infty)$ symmetry manifests itself through the entanglement of subsystems with the rest of the Universe, and demonstrate irrelevance of geometry of the parameter space for observables. Hence, $SU(\infty)$-QGR deviates from gauge-gravity duality models, because the classical spacetime is an emergent effective geometry with negative signature, reflecting relative variation of quantum states of subsystems and quantum uncertainties. We also briefly discuss $SU(\infty)$-QGR specific models for dark energy.

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