Work out the evolution of the k=0 covariant background

Derive the time evolution of the k=0 covariant quantum-spacetime background and determine its cosmological behavior within the dynamical IKKT model.

Background

The paper states that analogous constructions exist for a spatially flat, k=0 FLRW background. Unlike the k=-1 case discussed in detail, the dynamical evolution of the k=0 solution has not been derived.

Resolving this issue would determine whether the spatially flat background can provide a physically viable cosmological solution and how its evolution compares with the k=-1 background.

References

Analogous statements apply to the $k=0$ background \, but its evolution has not yet been worked out.

— Quantum spacetime and gravity from the IKKT matrix model: an invitation  (2609.08955 - Steinacker, 8 Sep 2026) in Section 4.4, “Dynamical covariant cosmological spacetime”