Radion Stabilization by Stringy Effects in General Relativity

TL;DR

This paper demonstrates that a gas of quantum strings can dynamically stabilize the size of extra dimensions in general relativity, leading to oscillations around the self-dual radius and consistent cosmological evolution.

Contribution

It introduces a novel string gas-based mechanism for radion stabilization within classical general relativity without violating energy conditions.

Findings

The radius of the extra dimension can oscillate around the self-dual radius.

Thermal equilibrium string gas stabilizes the compact dimension at the self-dual radius.

The stabilization mechanism aligns with observational bounds and does not require matter violating energy conditions.

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. 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. We show that our radion stabilization mechanism requires a stringy realization of inflation as scalar field driven inflation invalidates our mechanism. We also show that our stabilization mechanism is consistent with observational bounds.