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) less than or similar to (HL)(2) less than or similar to (rho(a) + rho(mu))/rho(m) where H is the Hubble parameter and rho(a), 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 less than or similar to 10 Omega(-2/3)(sigma 0) kpc and a characteristic velocity v(0) less than or similar to 10(-5) Omega(-2/3)(sigma 0) 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) similar to 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. (C) 2010 Elsevier B.V. All rights reserved.