If the dark sector contains 't Hooft-Polyakov monopoles and a small enough dark gauge coupling, dark monopoles could be a macroscopic dark matter candidate. Its Higgs-portal coupling to the Standard Model can modify the electroweak vacuum in the monopole interior. In the most striking cases, dark monopoles could even contain electroweak-symmetric cores and generate multi-hit signals at large-volume detectors. If they are produced via parametric resonance in the early Universe, monopoles with radii up to one micron and masses up to ten kilotonnes could account for all of dark matter.
Our electroweak vacuum may be metastable in light of the current experimental data of the Higgs/top quark mass. If this is really the case, high-scale inflation models require a stabilization mechanism of our vacuum during inflation. A possible candidate is the Higgs-inflaton/-curvature coupling because it induces an additional mass term to the Higgs during the slow roll regime. However, after the inflation, the additional mass term oscillates, and it can potentially destabilize our electroweak vacuum via production of large Higgs fluctuations during the inflaton oscillation era. In this paper…
Recently Garcia Bellido et. al. have proposed that electroweak baryogenesis may occur at the end of inflation, in a scenario where the reheat temperature is too low for electroweak symmetry restoration. I show why the scenario is difficult to test reliably by classical field techniques on the lattice.
Two recent scenarios of preheating-related baryogenesis are compared within the framework of Abelian Higgs model in (1+1) dimensions. It is shown that they shift baryon number in opposite directions. Once both scenarios can realize simultaneously as overlapped stages of the same physical process, even the sign of net generated asymmetry becomes dependent on initial parameters.
It has recently been suggested that the baryon washout problem of standard electroweak baryogenesis could be avoided if inflation ends at a low enough energy density and a parametric resonance transfers its energy repidly into the standard model fields. We present preliminary results of numerical simulations in a SU(2)xU(1) gauge-Higgs model in which this process was studied.
The origin of the matter-antimatter asymmetry remains one of the most fundamental problems of cosmology. In this talk I present a novel scenario for baryogenesis at the electroweak scale, without the need for a first order phase transition. It is based on the out of equilibrium resonant production of long wavelength Higgs and gauge configurations, at the end of a period of inflation, which induces a large rate of sphaleron transitions, before thermalization at a temperature below critical.
In many inflationary models, a large amount of energy is transferred rapidly to the long-wavelength matter fields during a period of preheating after inflation. We study how this changes the dynamics of the electroweak phase transition if inflation ends at the electroweak scale. We simulate a classical SU(2)xU(1)+Higgs model with initial conditions in which the energy is concentrated in the long-wavelength Higgs modes. With a suitable initial energy density, the electroweak symmetry is restored non-thermally but broken again when the fields thermalize. During this symmetry restoration, baryon …
We consider the out-of-equilibrium (quasi-) particle number distributions of the Higgs and W-fields during electroweak tachyonic preheating. We model this process by a fast quench, and perform classical real-time lattice simulations in the SU(2)-Higgs model in three dimensions. We discuss how to define particle numbers and effective energies using two-point functions in Coulomb and unitary gauge, and consider some of the associated problems. After an initial exponential growth in effective particle numbers, the system stabilises, allowing us to extract effective masses, temperatures and chemic…
We refine the implementation of ensemble fermions for the electroweak sector of the Standard Model, introduced previously. We consider the behavior of different observables as the size of the ensemble is increased and show that the dynamics converges for ensemble sizes small enough that simulations of the entire electroweak sector become numerically tractable. We apply the method to the computation of the effective preheating temperature during a fast electroweak transition, relevant for Cold Electroweak Baryogenesis. We find that this temperature is never below 20 GeV, and this in combination…
We study out-of-equilibrium quasi-particle distributions of the Higgs and W fields during the zero-temperature tachyonic electroweak transition that has been assumed in recent scenarios of baryogenesis. Approximating the process by a fast quench, we perform classical real-time lattice simulations in the SU(2)-Higgs model. The emerging quasi-particle numbers and energies are then used to determine the effective temperatures, chemical potentials and masses of the particles shortly after the transition.
We explore viable scenarios for parametric resonant amplification of electroweak (EW) gauge fields and Chern-Simons number during preheating, leading to baryogenesis at the electroweak (EW) scale. In this class of scenarios time-dependent classical EW gauge fields, essentially spatially-homogeneous on the horizon scales, carry Chern-Simons number which can be amplified by parametric resonance up to magnitudes at which unsuppressed topological transitions in the Higgs sector become possible. Baryon number non-conservation associated with the gauge sector and the highly non-equilibrium nature of…
We consider a scenario in which the baryon asymmetry was created in the early universe during a cold electroweak transition. The spinodal instability of the Higgs field caused by a rapid change of sign of its effective mass-squared parameter induces tachyonic preheating. We study the development of Chern-Simons number in this transition by numerical lattice simulations of the SU(2)-Higgs model with an added effective CP-violating term. A net asymmetry is produced, and we study its dependence on the size of CP violation and the ratio of Higgs to W mass.
Current measurements of Standard Model parameters suggest that the electroweak vacuum is metastable. This metastability has important cosmological implications, because large fluctuations in the Higgs field could trigger vacuum decay in the early universe. For the false vacuum to survive, interactions which stabilize the Higgs during inflation -- e.g., inflaton-Higgs interactions or non-minimal couplings to gravity -- are typically necessary. However, the post-inflationary preheating dynamics of these same interactions could also trigger vacuum decay, thereby recreating the problem we sought t…
We consider the creation of non-zero Chern-Simons number in a model of the early Universe, where the Higgs field experiences a fast quench at the end of inflation and subsequently rolls down its potential barrier. Neglecting the expansion, we perform numerical lattice simulations in the Abelian Higgs model in 1+1 dimensions with an added phenomenological C and P violating term during this stage of so-called tachyonic preheating. The results suggest that even the sign of the Chern-Simons and thus baryon number is dependent on the ratio of the Higgs to W mass. We also discuss the appropriate cho…
We study the generation of magnetic fields during preheating within an scenario of hybrid inflation at the electroweak (EW) scale. We find that the non-perturbative and strongly out-of-equilibrium process of magnetic field production occurs along the lines predicted by Vachaspati many years ago. The system starts in the false vacuum at the end of inflation, and very quickly the initial quantum fluctuations of the Higgs field get amplified via long wavelength spinodal instabilities. The subsequent nucleation of the random Gaussian Higgs field bubbles (lumps) leads to EW symmetry breaking, and t…
Small evaporating black holes were proposed to be dangerous inducing fast decay of the electroweak false vacuum. We observe that the flat-spectrum matter perturbations growing at the post-inflationary matter dominated stage can produce such black holes in a tiny amount which may nevertheless be sufficient to destroy the vacuum in the visible part of the Universe via the induced process. If the decay probability in the vicinity of Planck-mass black holes was of order one as suggested in literature, the absence of such objects in the early Universe would put severe constraints on inflation and s…
We describe electroweak monopoles within the Born-Infeld extension of $SU(2)_L\times U(1)_Y$ electroweak theory. We argue for topological stability of these monopoles and computed their mass in terms of the Born-Infeld mass parameters. We then propose a new mechanism for electroweak baryogenesis which takes advantage of the following salient features of the electroweak monopoles: (i) monopoles support extra CP violation in the topological sector of the electroweak theory; (ii) they mediate unsuppressed baryon number violating interactions; (iii) non-thermal production of monopoles during the e…
We present a novel scenario for baryogenesis in a hybrid inflation model at the electroweak scale, in which the Standard Model Higgs field triggers the end of inflation. One of the conditions for successful baryogenesis, the departure from thermal equilibrium, is naturally achieved at the stage of preheating after inflation. The inflaton oscillations induce large occupation numbers for long-wavelength configurations of Higgs and gauge fields, which leads to a large rate of sphaleron transitions. We estimate this rate during the first stages of reheating and evaluate the amount of baryons produ…
We study the stability of the electroweak vacuum during and after the Starobinsky inflation, assuming the existence of the non-minimal Higgs coupling to the Ricci scalar. In the Starobinsky inflation, there exists $R^2$ term (with $R$ being the Ricci scalar), which modifies the evolution equation of the Higgs field. We consider the case that the non-minimal coupling is sizable so that the quantum fluctuation of the Higgs field is suppressed and that the Higgs amplitude is settled near the origin during the inflation. In such a case, the Higgs amplitude may be amplified in the preheating epoch …
We analyze the generation of helical magnetic fields during preheating in a model of low-scale electroweak (EW) hybrid inflation. We show how the inhomogeneities in the Higgs field, resulting from tachyonic preheating after inflation, seed the magnetic fields in a way analogous to that predicted by Vachaspati and Cornwall in the context of the EW symmetry breaking. At this stage, the helical nature of the generated magnetic fields is linked to the non-trivial winding of the Higgs-field. We analyze non-perturbatively the evolution of these helical seeds through the highly non-linear stages of s…
We maintain that the search for the electroweak monopole is a key issue in the advancement of our understanding of the standard model. Unlike the Dirac monopole in electrodynamics, which is optional, the electroweak monopole should exist within the framework of the standard model. The mass of the electroweak monopole is estimated to be 5 to 7 TeV, but could be as large as 15 TeV. Above threshold its production rate at the LHC is expected to be relatively large, (1/alpha(em)2) times bigger than that of W+W- pairs. The search for the electroweak monopole is one of the prime motivations of the ne…
We examine the issue of monopole annihilation at the electroweak scale induced by flux tube confinement, concentrating first on the simplest possibility---one which requires no new physics beyond the standard model. Monopoles existing at the time of the electroweak phase transition may trigger $W$ condensation which can confine magnetic flux into flux tubes. However we show on very general grounds, using several independent estimates, that such a mechanism is impotent. We then present several general dynamical arguments constraining the possibility of monopole annihilation through any confinin…
We consider an isolated electroweak monopole solution within the Standard Model with a non-linear Born-Infeld extension of the hypercharge gauge field. Monopole (and dyon) solutions in such an extension are regular and their masses are predicted to be proportional to the Born-Infeld mass parameter. We argue that cosmological production of electroweak monopoles may delay the electroweak phase transition and make it more strongly first order for monopole masses $M\gtrsim 9.3\cdot 10^3$ TeV, while the nucleosynthesis constraints on the abundance of relic monopoles impose the bound $M\lesssim 2.3\…
We present finite energy analytic monopole and dyon solutions whose size is fixed by the electroweak scale. Our result shows that genuine electroweak monopole whose mass is around 6.7 TeV could exist, which could be detected at LHC.
The vacuum manifold of the standard electroweak model is a three-sphere when one considers homogeneous Higgs field configurations. For inhomogeneous configurations we argue that the vacuum manifold is the Hopf fibered three sphere and that this viewpoint leads to general criteria to detect electroweak monopoles and Z-strings. We extend the Kibble mechanism to study the formation of electroweak monopoles and strings during electroweak symmetry breaking. The distribution of magnetic monopoles produces magnetic fields that have a spectrum $B_λ\propto λ^{-2}$, where $λ$ is a smearing length scale.…
We discuss the cosmological production and the successive evolution of the electroweak (Cho-Maison) monopole in the standard model, and estimate the remnant monopole density at present universe. We confirm that, although the electroweak phase transition is of the first order, it is very mildly the first order. So the monopole production comes from the thermal fluctuations of the Higgs field after the phase transition, not the vacuum bubble collisions during the phase transition. Moreover, while the monopoles are produced copiously around the Ginzburg temperature $T_G\simeq 59.6~{\rm TeV}$, mos…
We present a finite-energy electroweak-monopole solution obtained by considering non-linear extensions of the hypercharge sector of the Electroweak Theory, based on logarithmic and exponential versions of electrodynamics. We find constraints for a class of non-linear extensions and also work out an estimate for the monopole mass in this scenario. We finally derive a lower bound for the energy of the monopole and discuss the simpler case of a Dirac magnetic charge.
The existence of a magnetic monopole, if it exists, remains elusive. Experimental searches have been carried out and are continuing in this quest. Of great uncertainty is the mass of the monopole which is model-dependent and ranging from some Grand Unified scale to the electroweak scale. In this paper, we propose a model where topologically stable, finite-energy monopoles {\em à la} 't Hooft-Polyakov could exist with a mass proportional to the electroweak scale. This comes about in a model of neutrino masses where right-handed neutrinos are {\em non-sterile} whose electroweak-scale Majorana ma…
These lectures start with an elementary introduction to the subject of magnetic monopoles which should be accesible from any physics background. In the Weinberg-Salam model of electroweak interactions, magnetic monopoles appear at the ends of a type of non-topological vortices called electroweak strings. These will also be discussed, as well as recent simulations of their formation during a phase transition which indicate that, in the (unphysical) range of parameters in which the strings are classically stable, they can form with a density comparable to topological vortices.
The Higgs-inflaton coupling plays an important role in the Higgs field dynamics in the early Universe. Even a tiny coupling generated at loop level can have a dramatic effect on the fate of the electroweak vacuum. Such Higgs-inflaton interaction is present both at the trilinear and quartic levels in realistic reheating models. In this work, we examine the Higgs dynamics during the preheating epoch, focusing on the effects of the parametric and tachyonic resonances. We use lattice simulations and other numerical tools in our studies. We find that the resonances can induce large fluctuations of …
We revisit the compatibility between the chaotic inflation, which provides a natural solution to the initial condition problem, and the metastable electroweak vacuum, which is suggested by the results of LHC and the current mass measurements of top quark and Higgs boson. It is known that the chaotic inflation poses a threat to the stability of the electroweak vacuum because it easily generates large Higgs fluctuations during inflation or preheating and triggers the catastrophic vacuum decay. In this paper, we propose a simple cosmological solution in which the vacuum is stabilized during chaot…
We investigated numerically properties of Nambu monopoles in lattice Electroweak theory at realistic values of $α$ and $θ_W$. Our choice of parameters of lattice Lagrangian corresponds to large values of the Higgs boson mass $M_H > 2 M_W$. We find that the density of Nambu monopoles cannot be predicted by the choice of the initial parameters of Electroweak theory and should be considered as the new external parameter of the theory. We also investigate the difference between the versions of Electroweak theory with the gauge groups $SU(2)\otimes U(1)$ and $SU(2)\otimes U(1)/Z_2$. We do not detec…
The recent MoEDAL experiment at LHC to detect the electroweak monopole makes the theoretical prediction of the monopole mass an urgent issue. We discuss different ways to estimate the mass of the electroweak monopole. We first present a scaling argument which indicates that the mass of the electroweak monopole to be around 4 TeV. To justify this we construct finite energy analytic dyon solutions which could be viewed as the regularized Cho-Maison dyon, modifying the coupling strengths of the electromagnetic interaction of $W$-boson in the standard model. Our result demonstrates that a genuine …
We considered the lattice electroweak theory at realistic values of $α$ and $θ_W$ and for large values of the Higgs mass. We investigated numerically the properties of topological objects that are identified with quantum Nambu monopoles. We have found that the action density near the Nambu monopole worldlines exceeds the density averaged over the lattice in the physical region of the phase diagram. Moreover, their percolation probability is found to be an order parameter for the transition between the symmetric and the broken phases. Therefore, these monopoles indeed appear as real physical ob…
Current measurements of the Higgs boson mass and top Yukawa coupling suggest that the effective Higgs potential develops an instability below the Planck scale. If the energy scale of inflation is as high as the GUT scale, inflationary quantum fluctuations of the Higgs field can easily destabilize the standard electroweak vacuum and produce a lot of AdS domains. This destabilization during inflation can be avoided if a relatively large nonminimal Higgs-gravity or inflaton-Higgs coupling is introduced. Such couplings generate a large effective mass term for the Higgs, which can raise the effecti…
We apply a generalized field ansatz to describe the spherically symmetric sector of classical solutions of the electroweak theory. This sector contains Abelian magnetic monopoles labeled by their magnetic charge $n=\pm 1,\pm 2,\ldots$, the non-Abelian monopole for $n=\pm 2$ found previously by Cho and Maison (CM), and also the electric oscillating solutions. All magnetic monopoles have infinite energy. We analyze their perturbative stability and use the method of complex spacetime tetrad to separate variables and reduce the perturbation equations to multi-channel Schroedinger-type eigenvalue p…
In the standard model, the electroweak Z-string can end on a Nambu monopole, whose mass is calculated to be 689 GeV from the current precise experimental data assuming the new particle with mass 125 GeV to be the Higgs boson. We study an extension of the standard model with additional singlet and triplet Higgs fields in the framework of N=1 supersymmetric field theory by using a D-brane configuration in type IIA string theory. We construct a D-brane configuration describing the electroweak symmetry breaking, and find a single D2-brane configuration describing a Z-string and a Nambu monopole at…
We construct the multi-charge generalizations for the electroweak magnetic monopole solution of Cho and Maison within a wide range of values of the magnetic charge. We use the same ansatz for the axially symmetric fields as the one previously employed to construct the electroweak sphalerons and compare the internal structure of monopoles with that of sphalerons. The monopoles have zero dipole moment but a finite quadrupole momentum that rapidly increases with growing magnetic charge. For large charges, the monopole configurations are strongly squashed and show inside a bubble of symmetric phas…
We examine models where massless chiral fermions with both "electric" and "magnetic" hypercharges could form condensates. When some of the fermions are also electroweak doublets such condensates can break the electroweak gauge symmetry down to electromagnetism in the correct way. Since ordinary hypercharge is weakly coupled at the TeV scale, magnetic hypercharge is strongly coupled and can potentially drive the condensation. Such models are similar to technicolor, but with hypercharge playing the role of the technicolor gauge group, so the standard model gauge group breaks itself. A heavy top …
We use the $SU(5)$ model to show the presence in grand unified theories of an electroweak monopole and a magnetic dumbbell ("meson") made up of a monopole-antimonopole pair connected by a $Z$-magnetic flux tube. The monopole is associated with the spontaneous breaking of the weak $SU(2)_L$ gauge symmetry by the induced vacuum expectation value of a heavy scalar $SU(2)_L$ triplet with zero weak hypercharge contained in the adjoint Higgs 24-plet. This monopole carries a Coulomb magnetic charge of $(3/4) (2π/e)$ as well as $Z$-magnetic charge, where $2π/e$ denotes the unit Dirac magnetic charge. …
3D electroweak sphalerons on the lattice are used as test configurations for definitions of various topological defects. In the maximally Abelian gauge they are shown to contain a symmetric array of Abelian monopoles and anti-monopoles connected by two kinds of Abelian vortex strings. Gauge-invariant lattice definitions of the Nambu monopole and the Z-vortex string are formulated which correspond to Abelian projection from the unitary gauge. The sphalerons contain in their core just one (non-Abelian) Nambu monopole-anti-monopole pair (connected by a Z-string) in an unstable saddle point bound …
In a recent paper, Cho, Kim and Yoon (CKY) have proposed a version of the SU(2) $\times$ U(1) Standard Model with finite-energy monopole and dyon solutions. The CKY model postulates that the effective U(1) gauge coupling $\to \infty$ very rapidly as the Englert-Brout-Higgs vacuum expectation value $\to 0$, but in a way that is incompatible with LHC measurements of the Higgs boson $H \to γγ$ decay rate. We construct generalizations of the CKY model that are compatible with the $H \to γγ$ constraint, and calculate the corresponding values of the monopole and dyon masses. We find that the monopol…
The measured values of the Higgs and top quark mass indicate that the electroweak vacuum is metastable if there is no new physics below the Planck scale. This is at odds with a period of high scale inflation. A non-minimal coupling between the Higgs field and the Ricci scalar can stabilize the vacuum as it generates a large effective Higgs mass during inflation. We consider the effect of this coupling during preheating, when Higgs modes can be produced very efficiently due to the oscillating Ricci scalar. We compute their effect on the effective potential and the energy density. The Higgs exci…
We consider an extension of the Standard Model that was proposed recently by one of the current authors (PQH), which admits magnetic monopoles with a mass of order of a few TeV. We impose, in addition to topological quantization in the SU(2) sector of the model, the Dirac Quantization Condition (DQC) required for consistency of the quantum theory of a charged electron in the presence of the monopole. This leads to the prediction ${\rm sin}^2θ_W = 1/4$, where $θ_W$ is the weak mixing angle at the energy scale set by the monopole mass. A leading-order renormalization-group analysis yields the va…
We consider the lattice realization of the Standard Model with an additional $Z_6$ symmetry. Numerical simulations were performed on the asymmetric lattice, which corresponds to the finite temperature theory. Our choice of parameters corresponds to large Higgs masses ($M_H > 90$ Gev). The phase diagram was investigated and has been found to be different from that of the usual lattice realization of the Standard Model. It has been found, that the confinement-deconfinement phase transition lines for the SU(2) and SU(3) fields coincide. The transition line between Higgs and symmetric deconfinemen…
We propose a minimal and self-contained model in non-compact flat five dimensions which localizes the Standard Model (SM) on a domain wall. Localization of gauge fields is achieved by the condensation of Higgs field via a Higgs dependent gauge kinetic term in five-dimensional Lagrangian. The domain wall connecting vacua with unbroken gauge symmetry drives the Higgs condensation which provides both electroweak symmetry breaking and gauge field localization at the same time. Our model predicts higher-dimensional interactions $|H|^{2n}(F_{μν})^2$ in the low-energy effective theory. This leads to …
Topological Stabilization via Higgs and $Z$-Boson Mediated Repulsions in Electroweak Monopole-Antimonopole Pairs
Southern Center for Nuclear Science Theory, Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所南方核科学理论中心）；School of Nuclear Science and Technology, University of Chinese Academy of Sciences（中国科学院大学核科学与技术学院）；School of Physics, Universiti Sains Malaysia（马来西亚理科大学物理学院）
We show how in the standard electroweak model three $SU(2)_L$ Nambu monopoles, each carrying electromagnetic (EM) and Z- magnetic fluxes, can merge (through Z-strings) with a single $U(1)_Y$ Dirac monopole to yield a composite monopole that only carries EM magnetic flux. Compatibility with the Dirac quantization condition requires this composite monopole to carry six quanta ($12 π/e$) of magnetic charge, independent of the electroweak mixing angle $θ_w$. The Dirac monopole is not regular at the origin and the energy of the composite monopole is therefore divergent. We discuss how this problem …
We study the properties of Nambu monopoles and Z-vortices in the 3D lattice SU(2) Higgs theory which represents the Standard Model at high temperature. We show that the densities of the Nambu monopoles and the Z-vortices are O(1) in the symmetric phase and generically small in the Higgs phase. Near to the critical Higgs mass and in the vicinity of the phase transition the densities are no more negligible in the broken phase. The percolation probability of the Z-vortex lines is found as a new disorder parameter for this phase transition. We conclude that the transition to the symmetric phase is…
We study the onset of symmetry breaking after hybrid inflation in a model having the field content of the SU(2) gauge-scalar sector of the standard model, coupled to a singlet inflaton. This process is studied in (3+1)-dimensions in a fully non-perturbative way with the help of lattice techniques within the classical approximation. We focus on the role played by gauge fields and, in particular, on the generation of Chern-Simons number. Our results are shown to be insensitive to the various cut-offs introduced in our numerical approach. The spectra preserves a large hierarchy between long and s…
