Establish the nonlinear gravitational dynamics

Establish the nonlinear gravitational dynamics of the IKKT matrix model on covariant quantum-spacetime backgrounds, including the physical significance of Yang–Mills-induced mirage matter and the role of higher-spin components.

Background

In this framework, the metric and frame are derived from matrix variables and generally contain higher-spin components. The effective gravitational action combines an induced Einstein–Hilbert term with a Yang–Mills-type matrix action and vacuum energy, producing nonlocal infrared modifications that differ from general relativity.

The paper provides a linearized description of the resulting mirage matter but explicitly leaves the nonlinear dynamics, the physical interpretation of that sector, the crossover scale, and the stability of the cosmological background unresolved.

References

In particular, the ''mirage matter'' arising from the Yang-Mills flux and its physical significance needs to be better understood at the non-linear level. This is tied to the crossover scale $m$ m-cross-def-1, whose actual size depends on the background but needs better understanding. Finally, stability of the cosmic background requires more detailed work taking into account vacuum energy .

— Quantum spacetime and gravity from the IKKT matrix model: an invitation  (2609.08955 - Steinacker, 8 Sep 2026) in Section 8, “Conclusion and outlook”