Understand the late-time evolution of dynamical covariant spacetime

Determine the late-time evolution of the dynamically stabilized covariant quantum-spacetime background, including whether its cosmology ends in a Big Crunch or develops a cyclic structure.

Background

The paper constructs a time-dependent, SO(3,1)-covariant matrix background whose one-loop vacuum energy produces an expanding cosmological solution with scale factor proportional to cosmic time over a long epoch. The intermediate-time behavior is described, but the asymptotic evolution is not determined.

Understanding the late-time behavior is important for deciding whether the background provides a stable cosmological solution or instead undergoes recollapse or repeated cycles.

References

This describes an expanding universe with $a(t) \propto t$ similar to the rigid case, although the late-time structure remains to be understood, possibly leading to a Big Crunch or a cyclic structure.

— 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”