Matrix Model Approach to Cosmology

TL;DR

This paper explores matrix models to generate cosmological solutions, revealing features like singularity resolution and transitions from inflation, with potential for realistic four-dimensional cosmologies.

Contribution

It introduces a systematic method to find rotationally invariant cosmological solutions in matrix models, including new solutions with desirable cosmological properties.

Findings

Generated open, closed, and static cosmologies from matrix models.

Found solutions describing smooth transitions from inflation to noninflationary phases.

Identified four-dimensional de Sitter and anti-de Sitter solutions with noncommutative structures.

Abstract

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. The solutions provide for a matrix resolution of cosmological singularities. The commutative limit reveals other desirable features, such as a solution describing a smooth transition from an initial inflation to a noninflationary era. Many of the $d=3$ solutions have analogues in higher dimensions. The case of $d=5$, in particular, has the potential for yielding realistic four-dimensional cosmologies in the continuum limit. We find four-dimensional de Sitter $dS^4$ or anti-de Sitter $AdS^4$ solutions when a totally antisymmetric term is included in the matrix action. A nontrivial Poisson structure is attached to these manifolds which represents the lowest order effect of noncommutativity. For the case of $AdS^4$, we find one particlular limit where the lowest order noncommutativity vanishes at the boundary, but not in the interior.