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, v²≲(HL)²≲(ρσ+ρμ)/ρm$v^2\lesssim {(HL)}^2\lesssim ({\rho }_{\sigma }+{\rho }_{\mu })/{\rho }_m$ where H   is the Hubble parameter and ρσ${\rho }_{\sigma }$, ρμ${\rho }_{\mu }$ and ρm${\rho }_m$ 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 $L_0\lesssim 10{\Omega }_{\sigma 0}^{-2/3}\text{kpc}$ and a characteristic velocity $v_0\lesssim {10}^{-5}{\Omega }_{\sigma 0}^{-2/3}$ where Ω_σ0=ρ_σ0/ρ_c0${\Omega }_{\sigma 0}={\rho }_{\sigma 0}/{\rho }_{c0}$ and ρc${\rho }_c$ is the critical density. In order to satisfy these constraints with Ω_σ0∼1${\Omega }_{\sigma 0}\sim 1$, ρ_m0${\rho }_{m0}$ would have to be at least 10 orders of magnitude larger than ρ_σ0${\rho }_{\sigma 0}$, 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.

Keywords
2010PhLB..689..145S

Physics Letters B
Volume 689, Number 4, Page 145
2010 May

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