Expanding universe as a classical solution in the Lorentzian matrix model for nonperturbative superstring theory

TL;DR

This paper explores classical solutions in a Lorentzian matrix model for superstring theory, showing how an expanding universe can emerge dynamically with specific symmetry properties and noncommutative features.

Contribution

It identifies a unique class of SO(3) symmetric classical solutions that model an expanding universe within the matrix model framework.

Findings

Classical solutions exhibit time-dependent expansion consistent with universe growth.

Space-space noncommutativity is zero, space-time noncommutativity appears later.

Classical solutions complement Monte Carlo results by describing early universe behavior.

Abstract

Recently we have shown by Monte Carlo simulation that expanding (3+1)-dimensional universe appears dynamically from a Lorentzian matrix model for type IIB superstring theory in (9+1)-dimensions. The mechanism for the spontaneous breaking of rotational symmetry relies crucially on the noncommutative nature of the space. Here we study the classical equations of motion as a complementary approach. In particular, we find a unique class of SO(3) symmetric solutions, which exhibits the time-dependence compatible with the expanding universe. The space-space noncommutativity is exactly zero, whereas the space-time noncommutativity becomes significant only towards the end of the expansion. We interpret the Monte Carlo results and the classical solution as describing the behavior of the model at earlier time and at later time, respectively.