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

TL;DR

This paper analyzes how string and monopole junctions affect domain wall networks and concludes that such networks cannot naturally account for dark energy without conflicting with observational constraints.

Contribution

It demonstrates that domain wall networks with junctions cannot be frustrated enough to explain dark energy without contradicting observational data.

Findings

Domain wall velocities are limited by junction densities.

Networks cannot have large enough length scales to impact dark energy significantly.

Observational constraints rule out domain walls as a major dark energy component.

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, $v^2 \lsim (HL)^2 \lsim (\rho_\sigma + \rho_\mu)/\rho_m$ 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 \Omega_{\sigma 0}^{-2/3} {\rm kpc}$ and a characteristic velocity $v_0 \lsim 10^{-5} \Omega_{\sigma 0}^{-2/3}$ where $\Omega_{\sigma 0}=\rho_{\sigma 0}/\rho_{c 0}$ and $\rho_c$ is the critical density. In order to satisfy these constraints with $\Omega_{\sigma 0} \sim 1$, $\rho_{m 0}$ 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.