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

  • Marcus Sperling
  • Harold C. SteinackerEmail author
Open Access
Regular Article - Theoretical Physics


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, truncated at n. 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.


M(atrix) Theories Models of Quantum Gravity Non-Commutative Geometry Higher Spin Gravity 


Open Access

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© The Author(s) 2019

Authors and Affiliations

  1. 1.Yau Mathematical Sciences CenterTsinghua UniversityBeijingChina
  2. 2.Faculty of PhysicsUniversity of ViennaViennaAustria

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