Noncommutative Mixmaster Cosmologies

TL;DR

This paper explores a noncommutative geometry extension of the classical mixmaster universe model, analyzing how noncommutativity influences cosmological dynamics and the spectral action's role in inflation.

Contribution

It introduces a novel noncommutative version of the mixmaster universe and examines its dynamical properties and implications for cosmological inflation.

Findings

Noncommutative geometry alters mixmaster dynamics.

Spectral action influences inflationary potential.

Exotic smooth structures emerge in the model.

Abstract

In this paper we investigate a variant of the classical mixmaster universe model of anisotropic cosmology, where the spatial sections are noncommutative 3-tori. We consider ways in which the discrete dynamical system describing the mixmaster dynamics can be extended to act on the noncommutative torus moduli, and how the resulting dynamics differs from the classical one, for example, in the appearance of exotic smooth structures. We discuss properties of the spectral action, focussing on how the slow-roll inflation potential determined by the spectral action affects the mixmaster dynamics. We relate the model to other recent results on spectral action computation and we identify other physical contexts in which this model may be relevant.