Higgs domain walls in the thermal background

Abstract

Most cosmological models predict that the universe was hot and dense at the early stages of it's evolution. In this paper we analyse the influence of the thermal bath of Standard Model particles on the dynamics of cosmological Higgs domain walls. This manuscript poses an extension of our earlier work in which we investigated the evolution of networks of Higgs domain walls neglecting the impact of temperature variation.Using the thermally corrected effective potential of Standard Model we have found that both the position of the local maximum h max separating minima and the width of domain walls strongly depend on temperature T . For temperatures higher than 10 10 GeV they respectively increase proportionally and decrease inverse proportionally to the increasing temperature. Thus, the energy scale of the problem follows the value of temperature.Our numerical lattice simulations based on the PRS algorithm reveal that Higgs domain walls in the presence of the background thermal bath are highly unstable and decay shortly after formation. Moreover we have found that the fraction of horizons produced by inflation in which Higgs field expectation value is higher then h max needs to be very low in order for the evolution of the network of the domain walls to end in the electroweak vacuum. This means that Higgs domain walls necessarily were very rare objects and their average energy density was very small. As a result, the domain walls can not significantly effect cosmological observables.

Stability of domain walls in models with asymmetric potentials

“…Observed strong dependence on the bias is consistent with our earlier observations [13][14][15] of the dynamics of domain walls of the Higgs field. We could easily produce networks of domain walls decaying into electroweak vacuum using biased initial distributions even though this vacuum is strongly disfavoured by both difference of values of the effective potential and asymmetry of it around the local maximum.…”

“…This leads to formation of the local maximum of the effective potential for the field strength of the order of zero of the running coupling (the position of the maximum is gauge dependent) and second deeper minimum at superplanckian field strengths. The dynamics of domain walls driven by this highly asymmetric potential was studied in details in [13][14][15]. It is worth stressing that even though Higgs field breaks the symmetry it is a gauge symmetry, thus all the minima of effective potential connected by the symmetry transformation are physically equivalent.…”

(P)reheating and gravitational waves in α-attractor models

“…In order to control the error made during numerical computation and verify the reliability of results we used an error indicator based on a priori error estimation to detect the breakdown of used time integration scheme. Similar technique was successfully used by one of us in the past [34][35][36][37] to control time step length in simulations of dynamics of cosmological domain walls. The rapid growth of the numerical estimate of the leading term in the expansion of the error of time integration in powers of time step displays failure of the used numerical scheme in resolving dynamics of the physical problem.…”