Extending the velocity-dependent one-scale model for domain walls

TL;DR

This study uses large-scale simulations to evaluate and improve the velocity-dependent one-scale model for domain walls, introducing variable parameters for better accuracy across different cosmological regimes.

Contribution

The paper extends the VOS model by incorporating velocity-dependent parameters and additional energy loss mechanisms, improving its accuracy in modeling domain wall network evolution.

Findings

The original VOS model cannot fully reproduce simulation results with constant parameters.

Introducing velocity-dependent parameters enhances the model's accuracy.

The extended model fits simulation data across various cosmological regimes.

Abstract

We report on an extensive study of the evolution of domain wall networks in Friedmann-Lema\^{\i}tre-Robertson-Walker universes by means of the largest currently available field-theory simulations. These simulations were done in $4096^3$ boxes and for a range of different fixed expansion rates, as well as for the transition between the radiation and matter eras. A detailed comparison with the velocity-dependent one-scale (VOS) model shows that this cannot accurately reproduce the results of the entire range of simulated regimes if one assumes that the phenomenological energy loss and momentum parameters are constants. We therefore discuss how a more accurate modeling of these parameters can be done, specifically by introducing an additional mechanism of energy loss (scalar radiation, which is particularly relevant for regimes with relatively little damping) and a modified momentum parameter which is a function of velocity (in analogy to what was previously done for cosmic strings). We finally show that this extended model, appropriately calibrated, provides an accurate fit to our simulations.