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, $v^2 \lsim (HL)^2 \lsim (ρ_σ+ ρ_μ)/ρ_m$ where $H$ is the Hubble parameter and $ρ_σ$, $ρ_μ$ and $ρ_m$ 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 $ L_0 \lsim 10 Ω_{σ0}^{-2/3} {\rm kpc}$ and a characteristic velocity $v_0 \lsim 10^{-5} Ω_{σ0}^{-2/3}$ where $Ω_{σ0}=ρ_{σ0}/ρ_{c 0}$ and $ρ_c$ is the critical density. In order to satisfy these constraints with $Ω_{σ0} \sim 1$, $ρ_{m 0}$ would have to be at least 10 orders of magnitude larger than $ρ_{σ0}$, 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.

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