Domain walls in the extensions of the Standard Model

Abstract

Our main interest is the evolution of domain walls of the Higgs field in the early Universe. The aim of this paper is to understand how dynamics of Higgs domain walls could be influenced by yet unknown interactions from beyond the Standard Model. We assume that the Standard Model is valid up to certain, high, energy scale $\Lambda$ and use the framework of the effective field theory to describe physics below that scale. Performing numerical simulations with different values of the scale $\Lambda$ we are able to extend our previous analysis and determine its range of validity. We study domain walls interpolating between the physical electroweak vacuum and the vacuum appearing at very high field strengths. These domain walls could be formed from non-homogeneous configurations of the Higgs field produced by quantum fluctuations during inflation or thermal fluctuations during reheating. Our numerical simulations show that evolution of Higgs domain walls is rather insensitive to interactions beyond the Standard Model as long as masses of new particles are grater than $10^{12}\ \textrm{GeV}$. For lower values of $\Lambda$ the RG improved effective potential is strongly modified at field strengths crucial to the evolution of domain walls. For instance its minima become degenerate for $\Lambda$ around $10^{11}\ \textrm{GeV}$. We find that even in the case when the minima of the potential are nearly degenerate Higgs domain walls decayed shortly after their formation for generic initial conditions. On the other hand, in simulations with specifically chosen initial conditions Higgs domain walls can live longer and enter the scaling regime. We also determine the energy spectrum of gravitational waves produced by decaying domain walls of the Higgs field. For generic initial field configurations the amplitude of the signal is too small to be observed in present and planned detectors.