Cosmological evolution of domain wall networks

Abstract

We have studied the cosmological evolution of domain wall networks in two, three and four spatial dimensions using high-resolution field theory simulations. The dynamical range and number of our simulations is larger than in previous works, but does not allow us to exclude previous hints of deviations to the naively expected scale-invariant evolution. These results therefore suggest that the approach of domain wall networks to linear scaling is a much slower process than that of cosmic strings, which has been previously characterized in detail.

Scaling properties of domain wall networks

“…One expects that this will have a small impact on the large scale dynamics of the domain walls, since a wall's integrated surface density (and surface tension) are independent of its thickness. In particular, this assumption should not affect the presence or absence of a scaling solution [5], provided one uses a minimum thickness [17]-we will briefly revisit this issue below. (For a detailed discussion of analogous issues in the context of cosmic strings see [21].…”

“…The evolution of domain walls networks has been previously studied, numerically, by a number of different authors [5,[13][14][15][16][17][18][19], who usually found some hints for deviations to the scale-invariant evolution. Since there are good reasons to expect this scale-invariant attractor [18,20], one may ask whether these deviations point to the presence of physical mechanisms not accounted for in analytic descriptions or if they are simply a consequence of the limited dynamical range of numerical simulations.…”

Low-cost fermions in classical field simulations

“…For fundamental strings this is a natural procedure, but for strings which are topological defects, microscopic physics plays a significant role in the decay mechanism of strings [19]. Explicit calculations have been made in the context of gauge strings in the Abelian Higgs model [17,19,20], global [21] and semilocal strings [22,23] as well as domain walls [24,25]. The relevance of these calculations have been recently highlighted by the discovery of possible traces of cosmic strings in the cosmic microwave background [23,26].…”

A Review of Gravitational Waves from Cosmic Domain Walls

“…Many numerical studies [37][38][39][40][41][42][43] confirm that the evolution of domain walls in this regime can be described by the scaling solution, in which their energy density evolves according to the simple scaling law ρ wall ∝ t −1 , and their typical size is given by the Hubble radius ∼ t. 2 An analytic method to calculate the evolution of domain walls was also proposed in Refs. [44,45], which again shows the existence of the scaling solution.…”