String windings in the early universe

TL;DR

This work investigates whether string winding modes can dynamically yield three large spatial dimensions in the early universe by modeling a dilaton-gravity cosmology on a nine-torus filled with a gas of excited strings. The authors develop analytic and numerical tools, including Boltzmann equations for winding and KK mode annihilations and a thermodynamic treatment of Hagedorn and radiation phases, to determine the late-time dimensional outcome. They find that while three large dimensions can emerge, such an outcome is not statistically favored and is sensitive to initial data and the dilaton evolution, which weakens annihilation cross-sections and promotes freeze-out. The results challenge the generality of the BV mechanism and point to the need for additional physics to robustly realize a 3+1 dimensional universe from string gas dynamics.

Abstract

We study string dynamics in the early universe. Our motivation is the proposal of Brandenberger and Vafa, that string winding modes may play a key role in decompactifying three spatial dimensions. We model the universe as a homogeneous but anisotropic 9-torus filled with a gas of excited strings. We adopt initial conditions which fix the dilaton and the volume of the torus, but otherwise assume all states are equally likely. We study the evolution of the system both analytically and numerically to determine the late-time behavior. We find that, although dynamical evolution can indeed lead to three large spatial dimensions, such an outcome is not statistically favored.

Figures (4)

• Figure 1: Average initial and final number of wrapped dimensions as a function of the initial coupling and initial volume, starting with $\dot{\varphi} = -1$ and evolved using the multiply-wound cross section. The volume is measured in units of $(2 \pi \sqrt{\alpha'})^9$.
• Figure 2: Illustrates the dependence on the initial value of $\dot{\varphi}$. Same as Fig. 1 except the simulations begin with $\dot{\varphi} = -0.15$.
• Figure 3: A histogram showing the distribution of the initial number of unwrapped dimensions for universes that end up three dimensional. Extracted from the data set used to generate Fig. 1.
• Figure 4: Histograms showing the distribution in the number of unwrapped dimensions at late times for various initial values of $\varphi$. Each histogram is based on $10^3$ simulations at an initial volume $V = 4.0 \times (2 \pi \sqrt{\alpha'})^9$ and an initial $\dot{\varphi} = -1$.