$SU(\infty )$ Quantum Gravity and Cosmology

Abstract

We highlight the structure and properties of an abstract approach to quantum cosmology and gravity, dubbed $SU(\infty )$-QGR. Beginning from the concept of the Universe as an isolated quantum system, the main axiom of is the existence of an infinite number of mutually commuting observables. Consequently, the Hilbert space of the Universe represents $SU(\infty )$ symmetry. This Universe as a whole is static and topological. Nonetheless, quantum fluctuations induce local clustering in its quantum state and divide it into approximately isolated subsystems representing $G\times SU(\infty )$, where $G$ is a generic finite-rank internal symmetry. Due to the global $SU(\infty )$ subsystems are entangled to the rest of the Universe. In addition to parameters characterizing the representation of $G$, their quantum states depend on four continuous parameters: two of them characterize the representation of $SU(\infty )$, a dimensionful parameter arises from the possibility of comparing representations of $SU(\infty )$ by different subsystems; the fourth parameter is a measurable used as time registered by an arbitrary subsystem chosen as a clock. It introduces a relative dynamics for subsystems, formulated by a symmetry-invariant effective Lagrangian defined on the (3+1)D space of the continuous parameters. At lowest quantum order, the Lagrangian is a Yang--Mills field theory for both $SU(\infty )$ and internal symmetries. We identify the common $SU(\infty )$ symmetry and its interaction with gravity. Consequently, $SU(\infty )$-QGR predicts a spin-1 mediator for quantum gravity (QGR). Apparently, this is in contradiction with classical gravity. Nonetheless, we show that an observer who is unable to detect the quantumness of gravity perceives its effect as curvature of the space of average values of the continuous parameters. We demonstrate Lorentzian geometry of this emergent classical spacetime.

19 pages; 1 figure; published version

References in corpus (33)

• Gauge Theory Correlators from Non-Critical String Theory
• Large N Field Theories, String Theory and Gravity
• M Theory As A Matrix Model: A Conjecture
• Quantifying Coherence
• The teleparallel equivalent of general relativity
• Remote quantum entanglement between two micromechanical oscillators
• Testing Einstein's special relativity with Fermi's short hard gamma-ray burst GRB090510
• Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
• Quantum speed limit for non-Markovian dynamics
• Quantum speed limits in open system dynamics
• Planck 2018 results. III. High Frequency Instrument data processing and frequency maps
• Quantum tensor product structures are observable-induced
• Space from Hilbert Space: Recovering Geometry from Bulk Entanglement
• The Trinity of Relational Quantum Dynamics
• Speed limit for open quantum systems
• Emergent Spacetime
• Riemann-Einstein Structure from Volume and Gauge Symmetry
• Lectures on Gravity and Entanglement
• Modified gravity: a unified approach
• How is quantum information localized in gravity?
• Action quantum speed limits
• Bulk Entanglement Gravity without a Boundary: Towards Finding Einstein's Equation in Hilbert Space
• Quantum Relativity of Subsystems
• Gravitational splitting at first order: Quantum information localization in gravity
• Quantum-first gravity
• Einstein Equation from Covariant Loop Quantum Gravity in Semiclassical Continuum Limit
• Physical Purification of Quantum States
• Gravity-Yang-Mills-Higgs unification by enlarging the gauge group
• Constraints on Lorentz invariance violation from the LHAASO observation of GRB 221009A
• Comparing Quantum Gravity Models: String Theory, Loop Quantum Gravity, and Entanglement gravity versus $SU(\infty )$-QGR
• Why Matrix theory works for oddly shaped membranes
• Making a Quantum Universe: Symmetry and Gravity
• Symmetry as a foundational concept in Quantum Mechanics

Cited by in corpus (1)

• Quantum state of fields in $SU(\infty )$ Quantum Gravity ($SU(\infty )$-QGR)