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Effective Field Theory Approach to String Gas Cosmology

Thorsten Battefeld, Scott Watson

TL;DR

This work examines how a closed string gas influences late-time cosmology through a 4D effective field theory. By deriving the 4D EFT from a higher-dimensional string-frame setup and translating to the Einstein frame, it shows that radion stabilization at the self-dual radius is robust only for a single extra dimension, with higher codimensions exhibiting slow radion roll. In the $d=1$ case, the radion dynamics yield a matter-like energy density and a potential dark-matter candidate, while also predicting a fifth-force–like modification of gravity. For $d>1$, the absence of a local minimum in the radion potential leads to slow-roll evolution and potential observational consequences, though stabilization is not achieved. Overall, the paper highlights the nuanced role of frame choice, dilaton dynamics, and string-mass modes in shaping late-time cosmology and dark matter phenomenology from string gases.

Abstract

We derive the 4D low energy effective field theory for a closed string gas on a time dependent FRW background. We examine the solutions and find that although the Brandenberger-Vafa mechanism at late times no longer leads to radion stabilization, the radion rolls slowly enough that the scenario is still of interest. In particular, we find a simple example of the string inspired dark matter recently proposed by Gubser and Peebles.

Effective Field Theory Approach to String Gas Cosmology

TL;DR

This work examines how a closed string gas influences late-time cosmology through a 4D effective field theory. By deriving the 4D EFT from a higher-dimensional string-frame setup and translating to the Einstein frame, it shows that radion stabilization at the self-dual radius is robust only for a single extra dimension, with higher codimensions exhibiting slow radion roll. In the case, the radion dynamics yield a matter-like energy density and a potential dark-matter candidate, while also predicting a fifth-force–like modification of gravity. For , the absence of a local minimum in the radion potential leads to slow-roll evolution and potential observational consequences, though stabilization is not achieved. Overall, the paper highlights the nuanced role of frame choice, dilaton dynamics, and string-mass modes in shaping late-time cosmology and dark matter phenomenology from string gases.

Abstract

We derive the 4D low energy effective field theory for a closed string gas on a time dependent FRW background. We examine the solutions and find that although the Brandenberger-Vafa mechanism at late times no longer leads to radion stabilization, the radion rolls slowly enough that the scenario is still of interest. In particular, we find a simple example of the string inspired dark matter recently proposed by Gubser and Peebles.

Paper Structure

This paper contains 8 sections, 37 equations, 2 figures.

Table of Contents

  1. Introduction
  2. String Gases in the string Frame
  3. String Gases in the Einstein Frame
  4. Switching Frames and Stability
  5. String Gases in Four Dimensional Einstein Gravity
  6. Late time solutions with $d=1$ and dark matter
  7. Late time solutions for $d>1$
  8. Conclusion

Figures (2)

  • Figure 1: The potential $\ln(V(\lambda,\varphi,\psi)/(V_d\mu))$ from (\ref{['potential']}) is plotted with $d=6$, $N_d=M_d=M_3=1$, $N_3=0$, $M_p\equiv 1$ and (a) the dilaton held constant at $\varphi=-3/M_p$, (b) the extra dimensions held constant at $\psi=0$ and (c) the large dimensions held constant at $\lambda=10$.
  • Figure 2: The solution to equations (\ref{['EOM1']})-(\ref{['EOM3']}) for the potential $V(\lambda,\varphi,\psi)$ from (\ref{['potential']}) as plotted in Fig. \ref{['pic:potential']} with the same settings and the initial conditions $\varphi=\dot{\varphi}=\psi=\dot{\psi}=\lambda=0$: (a) evolution of $\lambda(t)$ (large dimensions, upper curve) and $\psi(t)$ (extra dimensions, lower curve), (b) evolution of the dilaton $\varphi(t)$.