We consider the Skyrme model modified by the addition of mass terms which explicitly break chiral symmetry and pick out a specific point on the model's target space as the unique true vacuum. However, they also allow the possibility of false vacua, local minima of the potential energy. These false vacuum configurations admit metastable skyrmions, which we call false skyrmions. False skyrmions can decay due to quantum tunnelling, consequently causing the decay of the false vacuum. We compute the rate of decay of the false vacuum due to the existence of false skyrmions.
We consider the classical static soliton solutions of the Skyrme model with false vacuum potential. We make use of fully three-dimensional relaxation calculations to construct global energy minimizers in the sectors of topological degrees from $Q=1$ to $Q=6$. These solutions may be metastable, they contain a domain of true vacuum inside the core. Further, we explore small regions of negative topological charge density which appear for the Skyrmions of degrees $Q=3,5,6$.
In planar (baby) Skyrme systems, there may be extended linear structures which resemble either domain walls or chains of skyrmions, depending on the choice of potential and boundary conditions. We show that systems with a single vacuum, for example with potential V=1-phi_3, admit chain solutions, whereas walls are ruled out by the uniqueness of the vacuum. On the other hand, in double-vacuum systems such as V=1/2*(1-phi_3^2), one has stable wall solutions, but there are no stable chains; the walls may be viewed as the primary objects in such systems, with skyrmions being made out of them.
Based on the observation that the skyrmion in Skyrme theory can be viewed as a dressed monopole, we show that the skyrmions have two independent topology, the baryon topology $π_3(S^3)$ and the monopole topology $π_2(S^2)$. With this we propose to classify the skyrmions by two topological numbers $(m,n)$, the monopole number $m$ and the shell (radial) number $n$. In this scheme the popular (non spherically symmetric) skyrmions are classified as the $(m,1)$ skyrmions but the spherically symmetric skyrmions are classified as the $(1,n)$ skyrmions, and the baryon number $B$ is given by $B=mn$. Mo…
We study the possibility of forming the false vacuum bubble nucleated within the true vacuum background via the true-to-false vacuum phase transition in curved spacetime. We consider a semiclassical Euclidean bubble in the Einstein theory of gravity with a nonminimally coupled scalar field. In this paper we present the numerical computations as well as the approximate analytical computations. We mention the evolution of the false vacuum bubble after nucleation.
We study the dynamics of false vacuum bubbles. A nonminimally coupled scalar field gives rise to the effect of negative tension. The mass of a false vacuum bubble from outside observer's point of view can be positive, zero, or negative. The interior false vacuum has de Sitter geometry, while the exterior true vacuum background can have geometry depending on the vacuum energy. We show that there exist expanding false vacuum bubbles without the initial singularity in the past.
We study the dynamics of false vacuum bubbles in the Brans-Dicke theory of gravity by using the thin shell or thin wall approximation. We consider a false vacuum bubble that has a different value for the Brans-Dicke field between the inside false vacuum region and the outside true vacuum region. Within a certain limit of field values, the difference of field values makes the effective tension of the shell negative. This allows new expanding false vacuum bubbles to be seen by the outside observer, which are disallowed in Einstein gravity.
In this work we consider kink-antikink and antikink-kink collisions in a modified $ϕ^4$ model with a false vacuum characterized by a dimensionless parameter $ε$. The usual $ϕ^4$ model is recovered for $ε=0$. We investigate the $ε<<1$ regime where the kink in the presence of false vacuum can be understood as a small deformation of the standard kink for the $ϕ^4$ model. We show that the attractive interaction between the kink-antikink pair leads to a rich scattering pattern, in some cases delaying considerably the false vacuum decay.
In the thin-wall approximation, the decay of a gravitating false vacuum to a lower-energy state is affected by the cosmological horizon structure in both spaces. The nucleation radius of a bubble of true vacuum depends on the surface tension of its boundary and equals the false vacuum cosmological horizon at a critical tension. We argue that there is no tunneling instanton solution beyond the critical tension and argue that there is therefore a bound on allowed membrane tension in theories which rely on semiclassical tunneling to relax the cosmological constant.
We consider a model where a scalar field develops a metastable vacuum state and weakly interacts with another scalar field. In this situation we find the probability of decay of the false vacuum stimulated by the presence and collisions of particles of the second field. The discussed calculation is an illustration of the recently suggested thermal approach to treatment of induced semiclassical processes.
This paper reexamines the question of vacuum decay in theories of quantum gravity. In particular it suggests that decay into stable flat or AdS vacua, never occurs. Instead, vacuum decay occurs, if at all, into a cosmological spacetime. If the latter has negative cosmological constant, it undergoes a Big Crunch, which suggests that the whole picture is inconsistent. The question of decay of de Sitter space must be very carefully defined.
We investigate and classify the possible types of false vacuum bubbles in Einstein gravity. The false vacuum bubbles can occur only if gravity is taken into account. We show that there exist solutions only with compact geometries. The analytic computations for the radius and nucleation rate of a vacuum bubble are evaluated using the thin-wall approximation. We discuss possible cosmological implications of our new solutions.
In this work we show a class of oscillating configurations for the evolution of the domain walls in Euclidean space. The solutions are obtained analytically. Phase transitions are achieved from the associated fluctuation determinant, by the decay rates of the false vacuum.
Motivated by the work of Mersini, the particle production related to the tunneling in false vacuum decay is carefully investigated in the thin-wall approximation. It is shown that in this case the particle production is exponentially suppressed even when the momentum is comparable to the curvature scale of the bubble. The number of created particles is ultraviolet finite.
In this presentation, we discuss the nucleation and subsequent evolution of false vacuum bubbles in the scalar-tensor gravity. First, we transform the scalar-tensor type theory of gravity to the standard Brans-Dicke type. Second, we transform the Brans-Dicke type theory from the Jordan frame to the Einstein frame. For a certain potential, a true vacuum bubble in the Einstein frame can be transformed to a false vacuum bubble in the Jordan frame by a conformal transformation. Thus, in the Jordan frame, the nucleation of a false vacuum bubble can be possible and its subsequent evolution can be de…
We construct a black hole whose interior is the false vacuum and whose exterior is the true vacuum of a classical field theory. From the outside the metric is the usual Schwarzschild one, but from the inside the space is de Sitter with a cosmological constant determined by the energy of the false vacuum. The parameters of the field potential may allow for the false vacuum to exist for more than the present age of the universe. A potentially relevant effective field theory within the context of QCD results in a Schwarzschild radius of about 200 km.
We calculate the three-point correlation function of the comoving curvature perturbation generated during an inflationary epoch driven by false vacuum energy. We get a novel false vacuum shape bispectrum, which peaks in the equilateral limit. Using this result, we propose a scenario which we call "old curvaton". The shape of the resulting bispectrum lies between the local and the false vacuum shapes. In addition we have a large running of the spectral index.
We study a gauge theory model where there is an intermediate symmetry breaking to a meta- stable vacuum that breaks a simple gauge group to a U (1) factor. Such models admit the existence of meta-stable magnetic monopoles, which we dub false monopoles. We prove the existence of these monopoles in the thin wall approximation. We determine the instantons for the collective coordinate that corresponds to the radius of the monopole wall and we calculate the semi-classical tunneling rate for the decay of these monopoles. The monopole decay consequently triggers the decay of the false vacuum. As the…
For the baby Skyrme model with a specific potential, compacton solutions, i.e., configurations with a compact support and parabolic approach to the vacuum, are derived. Specifically, in the non-topological sector, we find spinning Q-balls and Q-shells, as well as peakons. Moreover, we obtain compact baby skyrmions with non-trivial topological charge. All these solutions may form stable multi-soliton configurations provided they are sufficiently separated.
We investigate dielectric branes in false vacua in Type IIB string theory. The dielectric branes are supported against collapsing by lower energy vacua inside spherical or tube-like branes. We claim that such branes can be seeds for semi-classical (or quantum mechanical) decay of the false vacua, which makes the life-time of the false vacua shorter. Also, we discuss a topology change of a bubble corresponding to the fuzzy monopole triggered by dissolving fundamental strings.
We consider radiative corrections to false vacuum decay within the framework of quantum mechanics for the general potential of the form 1/2 M q^2 (q-A)(q-B), where M , A and B are arbitrary parameters. For this type of potential we provide analytical results for Green function in the background of corresponding bounce solution together with one loop expression for false vacuum decay rate. Next, we discuss the computation of higher order corrections for false vacuum decay rate and provide numerical expressions for two and three loop contributions.
We study a false vacuum decay in a two-dimensional black hole spacetime background. The decay rate in the case that nucleation site locates at a black hole center has been calculated in the literature. We develop a method for calculating the decay rate of the false vacuum for a generic nucleation site. We find that the decay rate becomes larger when the nucleation site is close to the black hole horizon and coincides with that in Minkowski spacetime when the nucleation site goes to infinity.
The abundance of the QCD axion is known to be suppressed if the Hubble parameter during inflation, $H_{\rm inf}$, is lower than the QCD scale, and if the inflation lasts sufficiently long. We show that the tight upper bound on the inflation scale can be significantly relaxed if the eternal old inflation is driven by the standard-model Higgs field trapped in a false vacuum at large field values. Specifically, $H_{\rm inf}$ can be larger than $100\,$GeV if the false vacuum is located above the intermediate scale. We also discuss the slow-roll inflation after the tunneling from the false vacuum t…
A procedure is reported for numerical analysis of false vacuum transition in a model with multiple scalar fields. It is a refined version of the approach by Konstandin and Huber. The alteration makes it possible to tackle a class of problems that was difficult or unsolvable with the original method, i.e. those with a distant or nonexistent true vacuum. An example with an unbounded-from-below direction is presented.
False vacuum decay around black holes: calculation from first principles in the (3+1)-dimensional case
Institute for Nuclear Research of the Russian Academy of Sciences（俄罗斯科学院核物理研究所）；Physics Faculty, Lomonosov Moscow State University（莫斯科国立大学物理系）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Institute for Theoretical and Mathematical Physics, MSU（莫斯科国立大学理论与数学物理研究所）
We find the novel effect on the decay of a false vacuum in view of quantum field theory, which is induced by a field coupling to the scalar field related to a first-order phase transition. This effect of the environment can never be included in the traditional method using the effective potential, and, in fact, acts as dissipative and fluctuation effects on tunneling phenomena. We show that the decay of the false vacuum is drastically either enhanced or suppressed. It is also clarified what kind of interaction enhance or suppress the tunneling probability.
I have calculated the exponential suppression factor in the decay rate of the false vacuum (per unit volume) for a real scalar field at finite temperature, in the presence of gravity, in the thin-wall approximation. Temperatures are assumed to be much greater than the inverse of the nucleation radius. The value of a local minimum of the scalar potential is arbitrary. Thus, both true and false vacuua may have arbitrary cosmological constants.
Recently it was discovered that the Standard Model vacuum may suffer an essential metastability near the Planck scale. In this regard it makes sense to study in more detail the decay processes of the metastable vacuum and to develop methods for their more accurate analysis. In this article we develop a technique to calculate two loop radiative corrections to false vacuum decay rate in thin-wall approximation and apply it to false vacuum decay in scalar quantum field theory with cubic and quartic interactions. The results obtained use dimensional regularization and given in two different renorm…
We study the stability of supersymmetry breaking vacuum in the presence of cosmic strings arising in the messenger sector. For certain ranges of the couplings, the desired supersymmetry breaking vacua become unstable against decay into phenomenologically unacceptable vacua. This sets constraints on the range of allowed values of the coupling constants appearing in the models and more generally on the chosen dynamics of gauge symmetry breaking.
Recent work is reported on inflation model building in the context of supergravity and superstrings, with special emphasis on False Vacuum (`Hybrid') Chaotic Inflation. Globally supersymmetric models do not survive in generic supergravity theories, but fairly simple conditions can be formulated which do ensure successful supergravity inflation. The conditions are met in some of the versions of supergravity that emerge from superstrings.
We consider the noncommutative Abelian-Higgs theory and construct new types of exact multi-vortex solutions that solve the static equations of motion. They in general do not follow from the BPS equations; only for some specific values of parameters, they satisfy the BPS equations saturating the Bogomol'nyi bound. We further consider the Abelian-Higgs theory with more complicated scalar potential allowing unstable minima and construct exact solutions of noncommutative false vacuum bubble with integer magnetic flux. The classical stability of the solutions is discussed.
We consider radiative corrections to false vacuum decay in a four-dimensional scalar field theory with cubic and quartic potential. Using planar thin wall approximation we were able to get analytical expression for the decay rate up to two loop order. The results obtained employ dimensional regularization and $\overline{MS}$ renormalization scheme.
This paper studies false vacuum lumps surrounded by the true vacuum in a real scalar field potential in flat spacetime. Fermions reside in the core of the lump, which are coupled with the scalar field via Yukawa interaction. Such lumps are stable against spherical collapse and deformation from spherical shape based on energetics considerations. The fermions inside the lump are treated as a uniform Fermi gas. We consider the Fermi gas in both ultrarelativistic and nonrelativistic limits. The mass and size of these lumps depend on the scale characterizing the scalar field potential as well as th…
We revisit the problem of decay of a metastable vacuum induced by the presence of a particle. For the bosons of the `master field' the problem is solved in any number of dimensions in terms of the spontaneous decay rate of the false vacuum, while for a fermion we find a closed expression for the decay rate in (1+1) dimensions. It is shown that in the (1+1) dimensional case an infrared problem of one-loop correction to the decay rate of a boson is resolved due to a cancellation between soft modes of the field. We also find the boson decay rate in the `sine-Gordon staircase' model in the limits …
We consider the decay of vortices trapped in the false vacuum of a theory of scalar electrodynamics in 2+1 dimensions. The potential is inspired by models with intermediate symmetry breaking to a metastable vacuum that completely breaks a U(1) symmetry, while in the true vacuum the symmetry is unbroken. The false vacuum is unstable through the formation of true vacuum bubbles; however, the rate of decay can be extremely long. On the other hand, the false vacuum can contain metastable vortex solutions. These vortices contain the true vacuum inside in addition to a unit of magnetic flux and the …
We investigate the role of nonperturbative, bubble-like inhomogeneities on the decay rate of false-vacuum states in two and three-dimensional scalar field theories. The inhomogeneities are induced by setting up large-amplitude oscillations of the field about the false vacuum as, for example, after a rapid quench or in certain models of cosmological inflation. We show that, for a wide range of parameters, the presence of large-amplitude bubble-like inhomogeneities greatly accelerates the decay rate, changing it from the well-known exponential suppression of homogeneous nucleation to a power-law…
We suggest a technique that explicitly accounts for the structure of an initial state of quantum field in the semiclassical calculations of path integral in curved space-time, and consider decay of metastable state (conformal vacuum of scalar particles above false classical vacuum) in background de Sitter space-time as an example. Making use of this technique, we justify the Coleman-De Luccia approach to the calculation of the decay probability. We propose an interpretation of the Hawking-Moss instanton as a limiting case of constrained instantons. We find that an inverse process of the transi…
We propose an interpretation of decays of a false vacuum into an $AdS$ region. The $AdS$ region is interpreted in terms of a dual field theory living on an end of the world brane which expands into the false vacuum.
We propose an ultracold atom analogue of early universe vacuum decay using all three states of a spin-1 Bose gas. We consider a one-dimensional system with both radio frequency and optical Raman coupling between internal states. An advantage of our proposal is the lack of a time-modulated coupling, which can lead to instabilities. Within the elaborate phase structure of the system we identify an effective Klein-Gordon field and use Gross-Pitaevskii simulations within the truncated Wigner approximation to model the decay of its false vacuum. We examine the dependence of the rate of vacuum decay…
We study the decay rate of a false vacuum in gauge theory at the one-loop level. We pay particular attention to the case where the bounce consists of an arbitrary number of scalar fields. With a multi-field bounce, which has a curved trajectory in the field space, the mixing among the gauge fields and the scalar fields evolves along the path of the bounce in the field space and the one-loop calculation of the vacuum decay rate becomes complicated. We consider the one-loop contribution to the decay rate with an arbitrary choice of the gauge parameter, and obtain a gauge invariant expression of …
The null result in the LHC may indicate that the standard model is not drastically modified up to very high scales such as the GUT/string scale. Having this in the mind, we suggest a novel leptogenesis scenario realized in the false vacuum of the Higgs field. If the Higgs field develops a large vacuum expectation value in the early universe, a lepton number violating process is enhanced, which we use for baryogenesis. To demonstrate the scenario, several models are discussed. For example, we show that the observed baryon asymmetry is successfully generated in the standard model with higher-dim…
We present a simple and intuitive description of both, the Schwinger effect and false vacuum decay through bubble nucleation, as tunneling problems in one-dimensional relativistic quantum mechanics. Both problems can be described by an effective potential that depends on a single variable of dimension length, which measures the separation of the particles in the Schwinger pair, or the radius of a bubble for the vacuum decay. We show that both problems can be described as tunneling in one-dimensional quantum mechanics if one interprets this variable as the position of a relativistic particle wi…
We investigate the nonlinear dynamics of cold atom systems that can in principle serve as quantum simulators of false vacuum decay. The analog false vacuum manifests as a metastable vacuum state for the relative phase in a two-species Bose-Einstein condensate (BEC), induced by a driven periodic coupling between the two species. In the appropriate low energy limit, the evolution of the relative phase is approximately governed by a relativistic wave equation exhibiting true and false vacuum configurations. In previous work, a linear stability analysis identified exponentially growing short-wavel…
The decay rate of a false vacuum is studied in gauge theory, paying particular attention to its gauge invariance. Although the decay rate should not depend on the gauge parameter $ξ$ according to the Nielsen identity, the gauge invariance of the result of a perturbative calculation has not been clearly shown. We give a prescription to perform a one-loop calculation of the decay rate, with which a manifestly gauge-invariant expression of the decay rate is obtained. We also discuss the renormalization necessary to make the result finite, and show that the decay rate is independent of the gauge p…
We point out that the (pseudo-)conformal Universe scenario may be realized as decay of conformally invariant, metastable vacuum, which proceeds via spontaneous nucleation and subsequent growth of a bubble of a putative new phase. We study perturbations about the bubble and show that their leading late-time properties coincide with those inherent in the original models with homogeneously rolling backgrounds. In particular, the perturbations of a spectator dimension-zero field have flat power spectrum.
The false vacuum decay has been a central theme in physics for half a century with applications to cosmology and to the theory of fundamental interactions. This fascinating phenomenon is even more intriguing when combined with the confinement of elementary particles. Due to the astronomical time scales involved, the research has so far focused on theoretical aspects of this decay. The purpose of this Letter is to show that the false vacuum decay is accessible to current optical experiments as quantum analog simulators of spin chains with confinement of the elementary excitations, which mimic t…
We provide a novel, concise and self-contained evaluation of true- and false vacuum decay rates in general relativity. We insist on general covariance and choose observable boundary conditions, which yields the well known false-vacuum decay rate and a new true-vacuum decay rate that differs significantly from prior work. The rates of true- and false vacuum decays are identical in general relativity. The second variation of the action has a negative mode for all parameters. Our findings imply a new perspective on cosmological initial conditions and the ultimate fate of our universe.
We study the effects of a fixed de Sitter geometry background in scenarios of false vacuum decay. It is currently understood that bubble nucleation processes associated with first order phase transitions are particularly important in cosmology. The geometry of spacetime complicates the interpretation of the decay rate of a metastable vacuum. However, the effects of curvature can still be studied in the particular case where backreaction is neglected. We compute the imaginary part of the action in de Sitter space, including the one-loop and the gradient corrections. We use two independent metho…
We analyse vacuum decay in rotating BTZ black hole spacetimes with the thin wall approximation. Possible parameter regions for the vacuum decay are clarified. We find that the nucleation rate is dominated by the bounce solution with the static shell configuration. The nucleation rate of the static shell decreases with the mass of the initial black hole. For a larger/smaller value of the initial black hole, the nucleation rate can be smaller/larger than that of the Coleman De Luccia vacuum decay in the pure AdS spacetime. Through the vacuum decay, the black hole gains its mass and loses the hor…
We analyze properties of unstable vacuum states from the point of view of the quantum theory. In the literature one can find some suggestions that some of false (unstable) vacuum states may survive up to times when their survival probability has a non-exponential form. At asymptotically late times the survival probability as a function of time $t$ has an inverse power--like form. We show that at this time region the energy of the false vacuum states tends to the energy of the true vacuum state as $1/t^{2}$ for $t \to \infty$. This means that the energy density in the unstable vacuum state shou…
In flat space and at finite temperature, there are two regimes of false vacuum decay in quantum field theory. At low temperature, the decay proceeds through thermally-assisted tunneling described by periodic Euclidean solutions -- bounces -- with non-trivial time dependence. On the other hand, at high temperature the bounces are time-independent and describe thermal jumps of the field over the potential barrier. We argue that only solutions of the second type are relevant for false vacuum decay catalyzed by a black hole in equilibrium with thermal bath. The argument applies to a wide class of …
We discuss an exact false vacuum decay rate at one loop for a real and complex scalar field in a quartic-quartic potential with two tree-level minima. The bounce solution is used to compute the functional determinant from both fluctuations. We obtain the finite product of eigenvalues and remove translational zero modes. The orbital modes are regularized with the zeta function and we end up with a complete renormalized decay rate. We derive simple expansions in the thin and thick wall limits and determine their validity.
