Radion Stabilization by Stringy Effects in General Relativity

TL;DR

Radion stabilization by a gas of strings is analyzed in General Relativity without a dilaton. By deriving the string-gas energy-momentum tensor and solving the Einstein equations, the authors show the radion can perform damped oscillations about the self-dual radius $R=\sqrt{\alpha'}$, and that a thermal string gas dynamically stabilizes the radius, allowing standard FRW cosmology for the large dimensions. The stabilization mechanism is shown to be incompatible with bulk scalar-field inflation, implying that either stringy inflation (e.g., via reheating-produced winding states) or an alternative early-Universe scenario is required. The work connects string thermodynamics to radion dynamics and delineates phenomenological bounds for the stabilizing gas, including implications for hot and cold dark matter components arising from massless and massive string states.

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.

Figures (1)

• Figure 1: Potential term for $n=-w= \pm1, N=1$. The horizontal axis is $b$ (in string units), the vertical axis gives the potential in units of ${\cal U}$, where ${\cal U}$ is the prefactor on the right hand side of (\ref{['pot']}).