Covariant cosmological quantum space-time, higher-spin and gravity in the IKKT matrix model

Abstract

We discuss a $(3+1)$-dimensional covariant quantum space-time describing a FLRW cosmology with Big Bounce, obtained by a projection of the fuzzy hyperboloid $H_n^4$. This provides a background solution of the IKKT matrix model with mass term. We characterize the bosonic fluctuation spectrum, which consists of a tower of higher-spin modes. The modes are organized in terms of an underlying $SO(4,2)$ structure group, which is broken to the $SO(3,1)$ isometry of the background. The resulting higher-spin gauge theory includes all degrees of freedom required for gravity, and should be well suited for quantization. All modes propagate with the same speed of light, even though local boost invariance is not manifest. The propagating metric perturbation modes comprise those of a massless graviton, as well as a scalar mode. Gauge invariance allows to obtain the analog of the linearized Einstein-Hilbert action, which is expected to be induced upon quantization.

46 + 12 pages. V2: references added, minor corrections. V3: improved presentation, references added, on-shell modes corrected. V4: incorrect statement on higher-spin truncation removed

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Cited by in corpus (23)

• On the propagation across the big bounce in an open quantum FLRW cosmology
• Gravity as a Quantum Effect on Quantum Space-Time
• On the quantum structure of space-time, gravity, and higher spin in matrix models
• Toward a twistor action for chiral higher-spin gravity
• Four-dimensional Gravity on a Covariant Noncommutative Space
• Higher-spin gravity and torsion on quantized space-time in matrix models
• Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
• Quantum (Matrix) Geometry and Quasi-Coherent States
• A Twistorial Description of the IKKT-Matrix Model
• Fermions on curved backgrounds of matrix models
• Cosmic time evolution and propagator from a Yang-Mills matrix model
• One-loop effective action and emergent gravity on quantum spaces in the IKKT matrix model
• One-loop effective action of the IKKT model for cosmological backgrounds
• $Sp(4;\mathbb{R})$ Squeezing for Bloch Four-Hyperboloid via The Non-Compact Hopf Map
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• The fuzzy BTZ
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