Scaling properties of domain wall networks

Abstract

We revisit the cosmological evolution of domain wall networks, taking advantage of recent improvements in computing power. We carry out high-resolution field theory simulations in two, three and four spatial dimensions to study the effects of dimensionality and damping on the evolution of the network. Our results are consistent with the expected scale-invariant evolution of the network, which suggests that previous hints of deviations from this behavior may have been due to the limited dynamical range of those simulations. We also use the results of very large (1024 3 ) simulations in three cosmological epochs to provide a calibration for the velocity-dependent one-scale model for domain walls: we numerically determine the two free model parameters to have the values cw = 0.5 ± 0.2 and kw = 1.1 ± 0.3.

Entropy production by domain wall decay in the NMSSM

“…On the other hand, there is another possibility that the dynamics after the domination would be frozen as suggested in Ref. [20], where ξ ∝ aðtÞ and ρ ∝ aðtÞ −1 are realized as in the nonrelativistic limit. We briefly discuss results for this latter case, too.…”

“…In fact, the dynamics of domain walls has been investigated and many detailed numerical simulations show that the dynamics of the domain wall network is relaxed at a late time to the so-called scaling regime, where the typical length scale ξ of the system stays of the Hubble radius H −1 [17][18][19][20][21][22]. Then, the energy density of domain walls also scales as [22] …”

“…(20) in the mirage mediation scenario. At H ≃ Γ moduli , the moduli decay at a moduli dominated universe produces gravitinos as…”

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.…”

“…[61], in Figure 4 we specify the parameter region of T ann and σ 1/3 relevant to observations. The colored regions in Figure 4 correspond to the parameter values for which the peak amplitude of GWs from domain walls [Equation (41)] exceeds the sensitivity curves plotted in Figure 3. In Figure 4, we also plot the parameter region denoted by "Wall domination", which corresponds to the potential uncertainties since the energy density of domain walls dominates the total energy density of the universe [see Equation (30)].…”