Impact of string and monopole-type junctions on domain wall dynamics: Implications for dark energy

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, v2≲(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 L0≲10Ωσ0−2/3kpc and a characteristic velocity v0≲10−5Ωσ0−2/3 where Ωσ0=ρσ0/ρc0 and ρc is the critical density. In order to satisfy these constraints with Ωσ0∼1, ρm0 would have to be at least 10 orders of magnitude larger than ρσ0, 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.