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Moduli Stabilization in String Gas Cosmology

Robert H. Brandenberger

TL;DR

Problem: stabilize moduli and explain why only three spatial dimensions grow large within a non-singular string-theory framework. Approach: formulate string gas cosmology with T-duality and a gas of winding and momentum modes in a dilaton-gravity background, and analyze radion and shape-moduli stabilization in both string and Einstein frames using massless string states. Contributions: explicit self-dual-radius stabilization mechanisms for radion and a harmonic-oscillator stabilization of the shape modulus, all arising from stringy dynamics and without fluxes or non-perturbative effects. Significance: establishes a concrete, non-singular path toward stabilized extra dimensions and sets the stage for connecting to late-time cosmology, inflation, or alternatives.

Abstract

String gas cosmology is an approach towards studying the effects of superstring theory on early universe cosmology which is based on new symmetries and new degrees of freedom of string theory. Within this context, it appears possible to stabilize the moduli which describe the size and shape of the extra spatial dimensions without the need of introducing many extra tools such as warping and fluxes. In this lecture, the recent progress towards moduli stabilization in string gas cosmology is reviewed, and outstanding problems for the scenario are discussed.

Moduli Stabilization in String Gas Cosmology

TL;DR

Problem: stabilize moduli and explain why only three spatial dimensions grow large within a non-singular string-theory framework. Approach: formulate string gas cosmology with T-duality and a gas of winding and momentum modes in a dilaton-gravity background, and analyze radion and shape-moduli stabilization in both string and Einstein frames using massless string states. Contributions: explicit self-dual-radius stabilization mechanisms for radion and a harmonic-oscillator stabilization of the shape modulus, all arising from stringy dynamics and without fluxes or non-perturbative effects. Significance: establishes a concrete, non-singular path toward stabilized extra dimensions and sets the stage for connecting to late-time cosmology, inflation, or alternatives.

Abstract

String gas cosmology is an approach towards studying the effects of superstring theory on early universe cosmology which is based on new symmetries and new degrees of freedom of string theory. Within this context, it appears possible to stabilize the moduli which describe the size and shape of the extra spatial dimensions without the need of introducing many extra tools such as warping and fluxes. In this lecture, the recent progress towards moduli stabilization in string gas cosmology is reviewed, and outstanding problems for the scenario are discussed.

Paper Structure

This paper contains 8 sections, 23 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Basics of String Gas Cosmology
  3. Moduli Stabilization in String Gas Cosmology
  4. Radion Stabilization in the String Frame
  5. Radion Stabilization in the Einstein Frame using Massless Modes
  6. Shape Moduli Stabilization
  7. Discussion
  8. Challenges for String Gas Cosmology

Figures (1)

  • Figure 1: Space-time diagram (sketch) showing the evolution of scales in inflationary cosmology. The vertical axis is time, and the period of inflation lasts between $t_i$ and $t_R$, and is followed by the radiation-dominated phase of standard big bang cosmology. During exponential inflation, the Hubble radius $H^{-1}$ is constant in physical spatial coordinates (the horizontal axis), whereas it increases linearly in time after $t_R$. The physical length corresponding to a fixed comoving length scale labelled by its wavenumber $k$ increases exponentially during inflation but increases less fast than the Hubble radius (namely as $t^{1/2}$) after inflation.