[Paper Review] Radion Stabilization by Stringy Effects in General Relativity and Dilaton Gravity

Subodh P. Patil, Robert Brandenberger|arXiv (Cornell University)|Jan 7, 2004

Cosmology and Gravitation Theories38 citations

TL;DR

This paper proposes a mechanism for dynamically stabilizing the radius of a compactified extra dimension using quantum effects from a gas of closed strings in general relativity and dilaton gravity. It shows that in thermal equilibrium, the radius naturally stabilizes at the self-dual radius without violating energy conditions, enabling a transition to standard Friedmann-Robertson-Walker cosmology, though it is incompatible with scalar field-driven bulk inflation.

ABSTRACT

We consider the effects of a gas of closed strings (treated quantum mechanically) on a background where one dimension is compactified on a circle. After we address the effects of a time dependent background on aspects of the string spectrum that concern us, we derive the energy-momentum tensor for a string gas and investigate the resulting space-time dynamics. We show that a variety of trajectories are possible for the radius of the compactified dimension, depending on the nature of the string gas, including a demonstration within the context of General Relativity (i.e. without a dilaton) of a solution where the radius of the extra dimension oscillates about the self-dual radius, without invoking matter that violates the various energy conditions. Our Mechanism is also valid for Dilaton Gravity. In particular, we find that in the case where the string gas is in thermal equilibrium, the radius of the compactified dimension dynamically stabilizes at the self-dual radius, after which a period of usual Friedmann-Robertson-Walker cosmology of the three uncompactified dimensions can set in. However, our radion stabilization mechanism is not consistent with having a period of scalar field driven bulk inflation.

Motivation & Objective

• To investigate how quantum effects from a gas of closed strings influence the dynamics of a compactified extra dimension.
• To determine whether radion stabilization can occur without invoking matter that violates energy conditions.
• To explore the viability of this mechanism in both general relativity and dilaton gravity frameworks.
• To assess compatibility with scalar field-driven bulk inflation.

Proposed method

• Model a background with one spatial dimension compactified on a circle, treating the string gas quantum mechanically.
• Analyze time-dependent background effects on the string spectrum relevant to the compactified dimension.
• Derive the energy-momentum tensor for the string gas in this compactified setting.
• Solve the resulting space-time dynamics using Einstein's equations in general relativity and dilaton gravity.
• Examine the behavior of the compactified radius under various string gas conditions, including thermal equilibrium.
• Investigate the consistency of the stabilization mechanism with scalar field-driven inflation in the bulk.

Experimental results

Research questions

• RQ1 Can the radius of a compactified dimension be dynamically stabilized without violating energy conditions?
• RQ2 What role does a quantum gas of closed strings play in stabilizing the radion in general relativity?
• RQ3 How does the stabilization mechanism behave in the context of dilaton gravity?
• RQ4 Does the mechanism allow for a transition to standard Friedmann-Robertson-Walker cosmology after stabilization?
• RQ5 Is the mechanism compatible with a period of scalar field-driven bulk inflation?

Key findings

• The radius of the compactified dimension stabilizes dynamically at the self-dual radius when the string gas is in thermal equilibrium.
• This stabilization occurs without requiring matter that violates any energy conditions, even in pure general relativity.
• The mechanism remains valid in dilaton gravity, indicating broad applicability across different gravity frameworks.
• After stabilization, the three non-compact dimensions can undergo a standard Friedmann-Robertson-Walker expansion.
• The mechanism is incompatible with a scalar field-driven period of bulk inflation.
• Oscillatory trajectories of the compactified radius are possible depending on the nature of the string gas, demonstrating dynamic behavior beyond static stabilization.