L. Sousa, P. P. Avelino

**Abstract**

We investigate the potential role of string and monopole-type junctions in the frustration of domain wall networks using a velocity-dependent one-scale model for the characteristic velocity, *v*, and the characteristic length, *L *, of the network. We show that, except for very special network configurations, v^{2}≲(HL)^{2}≲(ρσ+ρμ)/ρm where *H * is the Hubble parameter and ρσ, ρμ and ρm are the average density of domain walls, strings and monopole-type junctions. We further show that if domain walls are to provide a significant contribution to the dark energy without generating exceedingly large CMB temperature fluctuations then, at the present time, the network must have a characteristic length and a characteristic velocity where Ω_{σ}_{0}=ρ_{σ}_{0}/ρ_{c}_{0} and ρc is the critical density. In order to satisfy these constraints with Ω_{σ}_{0}∼1, ρ_{m}_{0} would have to be at least 10 orders of magnitude larger than ρ_{σ}_{0}, which would be in complete disagreement with observations. This result provides very strong additional support for the conjecture that no natural frustration mechanism, which could lead to a significant contribution of domain walls to the dark energy budget, exists.

**Keywords**

2010PhLB..689..145S

**Physics Letters B**

Volume 689, Number 4, Page 145

2010 May