Modular curves, C* algebras, and chaotic cosmology

TL;DR

This paper explores the connection between chaotic cosmological models, specifically the mixmaster universe, and the mathematical frameworks of modular curves and noncommutative geometry, highlighting the role of C*-algebras in describing solution dynamics.

Contribution

It introduces a novel link between chaotic cosmology and noncommutative geometry through the use of Cuntz-Krieger C*-algebras to model solution spaces.

Findings

Dynamical properties of solutions with bounded cycles are characterized.

The moduli space of solutions is described using noncommutative geometric tools.

A connection between chaotic cosmology and modular curves is established.

Abstract

We make some brief remarks on the relation of the mixmaster universe model of chaotic cosmology to the geometry of modular curves and to noncommutative geometry. In particular we consider a class of solutions with bounded number of cycles in each Kasner era and describe their dynamical properties, which we relate to the noncommutative geometry of a moduli space of such solutions, given by a Cuntz-Krieger C*-algebra.