Is there chaos in string cosmology?

TL;DR

This paper investigates Bianchi type IX string cosmologies and finds that, unlike in general relativity, chaos does not occur at the tree-level, with oscillations ending after finite sequences due to duality symmetry.

Contribution

It demonstrates the absence of chaos in string cosmology Bianchi IX models at tree-level, contrasting with general relativity, and explores the implications of duality symmetry on cosmic evolution.

Findings

No infinite chaotic oscillations in Einstein frame.

Finite oscillations cease when all expansion rates become positive.

Chaotic behaviour is incompatible with duality symmetry as t approaches zero.

Abstract

Bianchi type IX, 'Mixmaster' universes are investigated in low-energy-effective-action string cosmology. We show that, unlike in general relativity, there is no chaos in these string cosmologies for the case of the tree-level action. The characteristic Mixmaster evolution through a series of Kasner epochs is studied in detail. In the Einstein frame an infinite sequence of chaotic oscillations of the scale factors on approach to the initial singularity is impossible, as it was in general relativistic Mixmaster universes in the presence of a massless scalar field. A finite sequence of oscillations of the scale factors described by approximate Kasner metrics is possible, but it always ceases when all expansion rates become positive. In the string frame the evolution through Kasner epochs changes to a new form which reflects the duality symmetry of the theory. Again, we show that chaotic oscillations must end after a finite time. The need for duality symmetry appears to be incompatible with the presence of chaotic behaviour as $t \to 0$. We also obtain our results using the Hamiltonian qualitative cosmological picture for Mixmaster models. We also prove that a time-independent pseudoscalar axion field $h$ is not admitted by the Bianchi IX geometry.