[Paper Review] Is There Chaos in Low-Energy String Cosmology?

John D. Barrow, Mariusz P. Da̧browski|arXiv (Cornell University)|Nov 7, 1997

Cosmology and Gravitation Theories1 citations

TL;DR

This paper investigates chaos in low-energy string cosmology using Bianchi type IX (Mixmaster) universes and finds that, unlike in general relativity, chaotic oscillations of scale factors do not persist indefinitely. Instead, the evolution through Kasner epochs terminates after a finite sequence due to duality symmetry and the structure of the tree-level effective action, preventing infinite chaotic behavior near the initial singularity.

ABSTRACT

Bianchi type IX, 'Mixmaster' universes are investigated in low-energyeffective -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 E-mail:J.D.Barrow...

Motivation & Objective

• To determine whether chaotic dynamics, as seen in general relativistic Mixmaster universes, persist in low-energy string cosmology.
• To analyze the behavior of Bianchi type IX universes under the tree-level effective action of string theory.
• To investigate the role of duality symmetry in modifying the dynamics of scale factor evolution near the initial singularity.
• To compare the Einstein and string frames in terms of oscillatory behavior and the possibility of infinite chaotic sequences.

Proposed method

• Analyzes the low-energy effective action of string theory, focusing on the tree-level approximation.
• Transforms the dynamics into the Einstein frame to compare with known general relativistic Mixmaster behavior.
• Applies the duality symmetry of string theory to the string frame, altering the form of Kasner epoch transitions.
• Studies the evolution of scale factors through successive Kasner epochs using approximate solutions.
• Evaluates the sign of expansion rates to determine when oscillatory behavior must cease.
• Uses the structure of the effective action to show that chaotic oscillations cannot continue indefinitely.

Experimental results

Research questions

• RQ1 Does the Mixmaster universe in low-energy string cosmology exhibit infinite chaotic oscillations like in general relativity?
• RQ2 How does duality symmetry in the string frame alter the dynamics of Kasner epoch transitions?
• RQ3 What determines the termination of oscillatory behavior in string cosmological models?
• RQ4 Can an infinite sequence of scale factor oscillations occur in the Einstein frame under string theory's effective action?
• RQ5 Under what conditions do all expansion rates become positive, signaling the end of oscillations?

Key findings

• Chaotic oscillations of the scale factors do not persist indefinitely in low-energy string cosmology, unlike in general relativity.
• In the Einstein frame, an infinite sequence of chaotic oscillations is impossible due to the structure of the effective action.
• A finite sequence of oscillations described by approximate Kasner metrics is possible, but ends when all expansion rates become positive.
• In the string frame, duality symmetry transforms the evolution through Kasner epochs into a new form that still prevents infinite chaos.
• The termination of oscillations occurs after a finite time, regardless of frame, due to the dynamics governed by the tree-level effective action.
• The presence of duality symmetry appears to be essential in suppressing infinite chaotic behavior in string cosmological models.