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Modified gravity at large scales on quantum spacetime in the IKKT model

Harold C. Steinacker

TL;DR

This work investigates gravity in the IKKT matrix model, showing that gravity emerges at one loop from a Yang–Mills-type action supplemented by an induced Einstein–Hilbert term. It introduces a nonlocal mirage energy-momentum tensor T_{μν}[C] that sources the metric in a modified, nonlocal Einstein equation, yielding dark-matter-like halos around localized matter and a gravitational crossover scale m separating GR-like short-distance behavior from a Yang–Mills–dominated IR regime. The analysis reveals a rich spectrum of propagating modes tied to higher-spin sectors, with potential IR instabilities that can be cured by including hs contributions and vacuum-energy effects. The results imply testable consequences for galaxy rotation curves and cosmic acceleration, while highlighting the need to incorporate axionic and dilatonic sectors and a fuller treatment of vacuum dynamics. Overall, the paper provides a framework for quantum emergent gravity on covariant quantum spacetime with intrinsic nonlocality and higher-spin structure, offering a route to connect matrix-model gravity with dark matter and dark energy phenomenology.

Abstract

The gravitational dynamics of 3+1 dimensional covariant quantum spacetime in the IKKT or IIB matrix model is studied at one loop, combining the Yang-Mills-type matrix action with the induced Einstein-Hilbert action. This combined action leads to interesting modifications of the gravitational dynamics at long distances, governed by modified Einstein equations including an extra geometrical tensor interpreted as ''mirage matter''. In particular we find extra non-Ricci flat geometric modes with a non-standard dispersion relation, with features reminiscent of dark matter.

Modified gravity at large scales on quantum spacetime in the IKKT model

TL;DR

This work investigates gravity in the IKKT matrix model, showing that gravity emerges at one loop from a Yang–Mills-type action supplemented by an induced Einstein–Hilbert term. It introduces a nonlocal mirage energy-momentum tensor T_{μν}[C] that sources the metric in a modified, nonlocal Einstein equation, yielding dark-matter-like halos around localized matter and a gravitational crossover scale m separating GR-like short-distance behavior from a Yang–Mills–dominated IR regime. The analysis reveals a rich spectrum of propagating modes tied to higher-spin sectors, with potential IR instabilities that can be cured by including hs contributions and vacuum-energy effects. The results imply testable consequences for galaxy rotation curves and cosmic acceleration, while highlighting the need to incorporate axionic and dilatonic sectors and a fuller treatment of vacuum dynamics. Overall, the paper provides a framework for quantum emergent gravity on covariant quantum spacetime with intrinsic nonlocality and higher-spin structure, offering a route to connect matrix-model gravity with dark matter and dark energy phenomenology.

Abstract

The gravitational dynamics of 3+1 dimensional covariant quantum spacetime in the IKKT or IIB matrix model is studied at one loop, combining the Yang-Mills-type matrix action with the induced Einstein-Hilbert action. This combined action leads to interesting modifications of the gravitational dynamics at long distances, governed by modified Einstein equations including an extra geometrical tensor interpreted as ''mirage matter''. In particular we find extra non-Ricci flat geometric modes with a non-standard dispersion relation, with features reminiscent of dark matter.
Paper Structure (40 sections, 180 equations, 4 figures)

This paper contains 40 sections, 180 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Minimal covariant quantum spacetime
  3. Spacetime algebra and realization
  4. Semi-classical description
  5. Effective geometry.
  6. Local description of covariant quantum spacetime
  7. Divergence-free frame and metric.
  8. Generalized cosmological background
  9. Metric and scales
  10. Modified Einstein equations and gravity
  11. Vacuum energy.
  12. Modified Einstein equations and non-local mirage matter
  13. Implications: dark (mirage) matter halo and extra modes
  14. Gravitational crossover scale.
  15. Background solution
  16. ...and 25 more sections

Figures (4)

  • Figure 1: Sketch of the bundle space ${\mathcal{M}}^{3,1}\times S^2$. The black lines indicate space-like $H^3$.
  • Figure 2: Gravitational potential (left) and rotation curves (right) for a point mass (yellow) and including the mirage halo (blue).
  • Figure 3: Kinetic action and unstable modes for $A(-k_0^2 + \vec{k}^2) (k_0^2 - \vec{k}^2/5 + 0.1)A$.
  • Figure 4: Kinetic action for stabilized modes $A((-k_0^2 + \vec{k}^2) (k_0^2 - \vec{k}^2/5 + 0.1) - 0.015 + 0.355 k_0^2)A\ $.