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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 $10^{10}\; \textrm{GeV}$ 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.

Quantum scale invariant regularization is a variant of dimensional regularization where the renormalization scale is treated as a dynamical field. But, rather than be regarded as a novel regularization method on par with dimensional regularization, momentum cutoff, Pauli-Villars etc., it should be understood as a way to define a subset in the infinite space of nonrenormalizable models of certain type. The subset realizes the demand that renormalization scale, along with any other dimensionful parameters, should be interpreted as a dynamical field's homogeneous background. This restriction is most straightforwardly implemented using dimensional regularization but it can hypothetically be imposed with any regularization method. Theories that satisfy it offer a new perspective on the radiative violation of global scale symmetry associated with RGE functions. As a result of the quantum scale invariant regularization being implemented, the scale symmetry is preserved at the quantum level despite the RGE functions being non-zero, as can be inspected at the level of composite quantum operators that govern dilatation of Green functions. We analyze these statements in explicit detail using a specific but easily generalized toy model with scalar fields., Comment: Some added commentary, extended bibliography, typos corrected

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.

We investigate the properties of vacuum decay taking into account a non-minimal coupling to gravity. We extend the standard thin-wall solution to include the non-minimal coupling and verify its validity by comparison with a full numerical study. We also investigate the implications of a~large cosmological constant whose influence on the geometry boosts the tunneling rate. Our analysis shows that the influence of the non-minimal coupling differs significantly between the cases of Minkowski and deSitter backgrounds., Comment: Corfu Summer Institute 2016 "School and Workshops on Elementary Particle Physics and Gravity"

We study domain walls which can be created in the Standard Model under the assumption that it is valid up to very high energy scales. We focus on domain walls interpolating between the physical electroweak vacuum and the global minimum appearing at very high field strengths. The creation of the network which ends up in the electroweak vacuum percolating through the Universe is not as difficult to obtain as one may expect, although it requires certain tuning of initial conditions. Our numerical simulations confirm that such domain walls would swiftly decay and thus cannot dominate the Universe. We discuss the possibility of detection of gravitational waves produced in this scenario. We have found that for the standard cosmology the energy density of these gravitational waves is too small to be observed in present and planned detectors.

We consider vacuum decay in the presence of a non-minimal coupling to gravity. We extend the usual thin-wall solution to include the non-minimal coupling. We also perform a full numerical study and discuss the validity of the new thin-wall approximation. Implications of a large cosmological constant, whose influence on the geometry boosts the tunnelling rate, are discussed. Our results show that the influence of the non-minimal coupling differs significantly between the cases of Minkowski and deSitter backgrounds. In the latter the decay probability quickly decreases when the coupling grows and in fact the vacuum can be made absolutely stable simply due to introduction of the non-minimal coupling. In the case of Minkowski background the effect is much weaker and the decay rate even increases for small values of the non-minimal coupling.

We explicitly show perturbative gauge fixing independence of the tunneling rate to a stable radiatively induced vacuum in the abelian Higgs model. We work with a class of $R_\xi$ gauges in the presence of both dimensionless and dimensionful gauge fixing parameters. We show that Nielsen identities survive the inclusion of higher order oparators and compute the tunnelling rate to the vacua modified by the nonrenormalisable operators in a gauge invariant manner. We also discuss implications of this method for the complete Standard Model.

Analysis of the Standard Model effective potential can reveal certain properties of the UV completion of SM. We discuss the issue of stability of the SM potential after inclusion of new nonrenormalizable interactions. We present the map of lifetimes resulting from different configurations of the new operators. The key result is proof of gauge independence of our results after inclusion of nonrenormalizable operators. We also discuss the consequences of RGE improvement of the potential., Comment: Talk given at 18th International Conference `From the Planck Scale to the Electroweak Scale', 25-29 May 2015, Ioannina, Greece

We explore the phenomenological predictions of a supersymmetric standard model, with a large extra dimension and unifying gauge couplings. The modified five dimensional renormalisation group equations make it possible to obtain light, maximally mixed stops, with a low scale of supersymmetry breaking and a low unification scale. This allows the fine-tuning to be lowered right down to the barrier coming directly from experimental lower limits on the stop masses. We also show that attempts at modifying the SUSY breaking pattern to obtain more natural soft terms at the high scale do not give the expected fine-tuning relaxation, and only RGE effects turn out to be effective in generating a lower fine-tuning.

Investigation of the structure of the Standard Model effective potential at very large field strengths opens a window towards new phenomena and can reveal properties of the UV completion of the SM. The map of the lifetimes of the vacua of the SM enhanced by nonrenormalizable scalar couplings has been compiled to show how new interactions modify stability of the electroweak vacuum. Whereas it is possible to stabilize the SM by adding Planck scale suppressed interactions and taking into account running of the new couplings, the generic effect is shortening the lifetime and hence further destabilisation of the SM electroweak vacuum. Absolute stability can be achieved by lowering the suppression scale of higher order operators while picking up such combinations of new couplings, which do not generate new deep minima in the potential. We discuss the issue of gauge dependence of the perturbative determination of the tunnelling rate and show how this rate can be made gauge independent at the leading nontrivial order of the RGE improved effective action., Comment: Proceedings of the Corfu Summer Institute 2014 "School and Workshops on Elementary Particle Physics and Gravity", 3-21 September 2014 Corfu, Greece

Investigation of the structure of the Standard Model effective potential at very large field strengths opens a window towards new phenomena and can reveal properties of the UV completion of the SM. The map of the lifetimes of the vacua of the SM enhanced by nonrenormalizable scalar couplings has been compiled to show how new interactions modify stability of the electroweak vacuum. Whereas it is possible to stabilize the SM by adding Planck scale suppressed interactions and taking into account running of the new couplings, the generic effect is shortening the lifetime and hence further destabilisation of the SM electroweak vacuum. These findings have been illustrated with phase diagrams of modified SM-like models. It has been demonstrated that stabilisation can be achieved by lowering the suppression scale of higher order operators while picking up such combinations of new couplings, which do not deepen the new minima of the potential. Our results show the dependence of the lifetime of the electroweak minimum on the magnitude of the new couplings, including cases with very small couplings (which means very large effective suppression scale) and couplings vastly different in magnitude (which corresponds to two different suppression scales)., Comment: plain Latex, 9 figures