String Cosmology and Chaos

TL;DR

This paper shows that string cosmology models based on Bianchi type IX universes do not exhibit the chaotic Mixmaster behavior near the initial singularity, contrasting with general relativity, due to string theory symmetries and dynamics.

Contribution

It demonstrates the absence of chaos in string cosmological Mixmaster models and explores how duality symmetry influences their evolution near singularities.

Findings

No Mixmaster chaos in string cosmologies with vanishing axion potential.

Finite oscillations of scale factors occur but cease as expansion rates become positive.

Chaotic oscillations are incompatible with duality symmetry as t approaches zero.

Abstract

We investigate Bianchi type IX ''Mixmaster'' universes within the framework of the low-energy tree-level effective action for string theory, which (when the ''stringy'' 2-form axion potential vanishes) is formally the same as the Brans-Dicke action with $\omega =-1$. We show that, unlike the case of general relativity in vacuum, there is no Mixmaster chaos in these string cosmologies. 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 stiff -fluid matter (or a massless scalar field). A finite sequence of oscillations of the scale factors approximated by 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 obtain our results using the Hamiltonian qualitative cosmological picture for Mixmaster models. We mention possible relations of this picture to diffeomorphism-independent methods of measuring chaos in general relativity. Finally, we discuss the effect of inhomogeneities and higher dimensions on the possible emergence of chaos within the string cosmology.