Signature change in matrix model solutions

TL;DR

This paper investigates classical solutions in Lorentzian matrix models, revealing that signature change is common and can model cosmological space-times with singularities, especially in four-dimensional non-commutative geometries.

Contribution

It demonstrates that signature change occurs in matrix model solutions and constructs toy cosmological models from non-commutative spaces, highlighting their potential in cosmology.

Findings

Signature change is common in solutions with quadratic and cubic terms.

Regions with Lorentzian signature can model cosmological singularities.

Four-dimensional models exhibit rapid expansion near initial singularities.

Abstract

Various classical solutions to lower dimensional IKKT-like Lorentzian matrix models are examined in their commutative limit. Poisson manifolds emerge in this limit, and their associated induced and effective metrics are computed. Signature change is found to be a common feature of these manifolds when quadratic and cubic terms are included in the bosonic action. In fact, a single manifold may exhibit multiple signature changes. Regions with Lorentzian signature may serve as toy models for cosmological space-times, complete with cosmological singularities, occurring at the signature change. The singularities are resolved away from the commutative limit. Toy models of open and closed cosmological space-times are given in two and four dimensions. The four dimensional cosmologies are constructed from non-commutative complex projective spaces, and they are found to display a rapid expansion near the initial singularity.