Cosmological String Gas on Orbifolds

TL;DR

This work examines whether pseudo-wound strings, which are contractible yet span the full spatial extent in spaces with trivial fundamental groups, can influence cosmology on toroidal orbifolds. Using a Smith–Vilenkin lattice framework adapted to orbifold group actions, the authors simulate string networks and measure unwinding times across various topologies, including supersymmetric and factored orbifolds, with both fixed and variable intercommutation probability $P$. They find that on many supersymmetric orbifolds the unwinding timescales can greatly exceed the Hubble time, implying a potential role in driving anisotropic expansion similarly to truly wound strings; the results depend sensitively on dimension, codimension of fixed points, and orbifold structure. The paper also outlines extensions to brane gases and Calabi–Yau compactifications, highlighting how brane wrapping and moduli dynamics could further shape the cosmological evolution of extra dimensions, and it emphasizes the need for dynamical spacetime studies that incorporate backreaction and stability analyses.

Abstract

It has long been known that strings wound around incontractible cycles can play a vital role in cosmology. In particular, in a spacetime with toroidal spatial hypersurfaces, the dynamics of the winding modes may help yield three large spatial dimensions. However, toroidal compactifications are phenomenologically unrealistic. In this paper we therefore take a first step toward extending these cosmological considerations to $D$-dimensional toroidal orbifolds. We use numerical simulation to study the timescales over which "pseudo-wound" strings unwind on these orbifolds with trivial fundamental group. We show that pseudo-wound strings can persist for many ``Hubble times'' in some of these spaces, suggesting that they may affect the dynamics in the same way as genuinely wound strings. We also outline some possible extensions that include higher-dimensional wrapped branes.

Figures (8)

• Figure 1: Positions and velocities of the string are evolved based on nearby positions and velocities from the previous timestep.
• Figure 2: (Left) Links in the string are constructed from three types of segments, moving at a velocity such that the combined energy (due to velocity and tension) in each is uniform. (Right) A typical string.
• Figure 3: Interactions are performed via intercommutation at a single point, which has been removed for clarity.
• Figure 4: Orbifolding takes a smooth geometry and creates singularities if the group action has fixed points. In these examples, we take $T^2 \rightarrow T^2 / \mathbb Z_2$ and $T^2 \rightarrow T^2 / \mathbb Z_4$.
• Figure 5: Typical initial winding configurations for $T^2$. For clarity we have only drawn 20 initially wound strings; in the simulations there were between 50 and 100.