Matrix Model Approach to Cosmology

Understand

We perform a systematic search for rotationally invariant cosmological solutions to matrix models, or more specifically the bosonic sector of Lorentzian IKKT-type matrix models, in dimensions $d$ less than ten, specifically $d=3$ and $d=5$.

• After taking a continuum (or commutative) limit they yield $d-1$ dimensional space-time surfaces, with an attached Poisson structure, which can be associated with closed, open or static cosmologies.
• For $d=3$, we obtain recursion relations from which it is possible to generate rotationally invariant matrix solutions which yield open universes in the continuum limit.
• Specific examples of matrix solutions have also been found which are associated with closed and static two-dimensional space-times in the continuum limit.