Biased Domain Walls and the Origin of Early Massive Structures

TL;DR

The paper investigates whether networks of domain walls from discrete symmetry breaking can seed early non-linear structures, contrasting standard walls, tightly constrained by the Zel'dovich bound $\sigma_{\rm Zel}$, with biased walls that decay early and may drive substantial structure formation. Using a parameter-free velocity-dependent one-scale model, the authors compute the final-wall decay energy $E_*$ via $E_* = 4\pi \varepsilon \sigma_{\rm Zel} a_*^2 \eta_*^2 C(\lambda)$ and the collapse-rate distribution $\frac{dN}{dz_*}$ in a $\Lambda$CDM background, including matter/radiation regimes and the transition at $z_{\rm eq}$. They translate $E_*$ into density perturbations through the Zel'dovich framework, deriving accreted masses up to $\sim 10^{15}\,M_\odot$ and a halo mass function showing standard walls are subdominant (fractions $\sim 10^{-9}$–$10^{-6}$ for the relevant mass ranges). For biased networks that decay around $z_{\rm bias}\sim 10^4$ with tensions near $\sigma\sim (65\ \,\mathrm{MeV})^3$, the model can reproduce JWST-reported mass excess at $z\gtrsim 7$, offering a testable alternative with weak gravitational-wave signatures and requiring broader sky surveys to fully validate the scenario.

Abstract

Discrete symmetry-breaking phase transitions in the early universe may have caused the formation of networks of sheet-like topological defects, usually referred to as domain walls, which separate regions that have settled into different vacuum states. Field theory simulations predict the successive collapse of increasingly larger domains, which could potentially leave observable imprints in present-day large-scale structures. We use a non-parametric analytical model to provide an estimate of the final decay energy of these walls and their associated collapse rate, as a function of redshift. The energy released by collapsing walls can act as a seed for density perturbations in the background matter field, influencing structure formation. We estimate the dependence of the current mass of the resulting non-linear objects on the collapse redshift and wall tension, showing that domain walls can contribute to the formation of objects as massive as present-day galaxy clusters. Still, we confirm that the contribution of standard domain walls to structure formation is subdominant. In contrast, biased domain walls - originating in models with an approximate (or biased) discrete symmetry breaking - generally face much less stringent constraints on their tension, which allows for significantly higher collapse energies. Based on our analysis, we are able to show that the collapse of such biased wall networks can provide a significant contribution to structure formation, and, in particular, a mass excess at $z \gtrsim 7$ as suggested by JWST data.

Figures (8)

• Figure 1: Dependence of the scale-invariant parameter $C$, defined in Eqs. \ref{['eqn:decayenergies']} and \ref{['eqn:Cpar']}, and the dimensionless collapse time $\tau_*$ on the expansion rate parameter $\lambda$. As $\lambda$ increases, Hubble damping becomes more efficient, leading to a longer wall collapse time.
• Figure 2: Evolution of the effective parameter $\lambda_{\rm eff}$, characterizing the instantaneous rate of expansion in a $\Lambda$CDM background. It can be seen that this approaches $\lambda=2/3$ in a matter-dominated and $\lambda=1/2$ in a radiation-dominated regime, respectively. At low redshift, a sharp growth of $\lambda_{\rm eff}$ is triggered when the universe enters the $\Lambda$-dominated era.
• Figure 3: Decay energies of individual wall collapses and their dependence on the decay redshift, $z_*$, and rescaled wall tension $\varepsilon=\sigma_{\rm w}/\sigma_{\rm Zel}$, where $\sigma_{\rm Zel}$ denotes the upper limit derived from the Zel'dovich bound. This plot displays the full numerical results (solid blue line) alongside the analytical approximations for the matter (red dashed line) and radiation eras (yellow dotted line) in Eqs. \ref{['eqn:energyparameters']} and \ref{['eqn:energyparameters2']}. The influence of the cosmological constant is visible at low redshift as a slight dampening of the expected available decay energy.
• Figure 4: Distribution of domain wall collapse events within the current horizon volume. The numerical result for a full $\Lambda$CDM universe is shown as a solid blue line, together with analytical approximations for the matter (red dashed line) and radiation (yellow dotted line) eras as given in Eqs. \ref{['eqn:distribution']} and \ref{['eqn:distribution2']}, respectively. Since the network becomes more and more diluted as the universe expands, the number density of collapse events decreases steeply as the collapse redshift $z_*$ decreases as well.
• Figure 5: Present-day masses of non-linear objects seeded by the collapse of standard domain walls at a redshift $z_*$ in units of solar mass $M_\odot$ ($\varepsilon=\sigma_{\rm w}/\sigma_{\rm Zel}$ is the wall tension, rescaled by the upper limit derived from the Zel'dovich bound). Our numerical result for a $\Lambda$CDM universe is shown as a solid blue line, together with the approximations for the matter (dashed red line) and radiation (yellow dotted line) eras given in Eqs. \ref{['eq:massmat']} and \ref{['eqn:massrad']}, respectively. The mass of these objects can reach up to $\sim 10^{15} M_\odot$, with the most massive ones being created by walls collapsing recently in cosmic history, when the collapse rate is lower.