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

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, $v^2 \lsim (HL)^2 \lsim (ρ_σ+ ρ_μ)/ρ_m$ where $H$ is the Hubble parameter and ${\rho }_{\sigma }$, ${\rho }_{\mu }$ and ${\rho }_m$ 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 ${\Omega }_{\sigma 0}={\rho }_{\sigma 0}/{\rho }_{c0}$ and ${\rho }_c$ is the critical density. In order to satisfy these constraints with ${\Omega }_{\sigma 0}\sim 1$, ${\rho }_{m0}$ would have to be at least 10 orders of magnitude larger than ${\rho }_{\sigma 0}$, 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.

4 pages, 1 figure

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