Metastable Vacuum State Research Articles

Multiverse as an Ensemble of Stable and Unstable Universes

Estimates of the Higgs and top quark masses, mH≃125.10±0.14 [GeV] and mt≃172.76±0.30 [GeV], based on the experimental result place the Standard Model in the region of the metastable vacuum. A consequence of the metastability of the Higgs vacuum is that it should induce the decay of the electroweak vacuum in the early Universe with catastrophic consequences. It may happen that certain universes were lucky enough to survive the time of canonical decay, that is the exponential decay, and live longer. This means that it is reasonable to analyze conditions allowing for that. We analyze the properties of an ensemble of universes with unstable vacua considered as an ensemble of unstable systems from the point of view of the quantum theory of unstable states. We found some symmetry relations for quantities characterizing the metastable state. We also found a relation linking the decay rate Γ of the metastable vacuum state with the Hubble parameter H(t), which may help to explain why a universe with an unstable vacuum that lives longer then the canonical decay times does not necessarily decay.

A universe born in a metastable false vacuum state needs not die

We try to find conditions, the fulfillment of which allows a universe born in a metastable false vacuum state to survive and not to collapse. The conditions found are in the form of inequalities linking the depending on time t instantaneous decay rate {varGamma }(t) of the false vacuum state and the Hubble parameter H(t). Properties of the decay rate of a quantum metastable states are discussed and then the possible solutions of the conditions found are analyzed and discussed. Within the model considered it is shown that a universe born in the metastable vacuum state has a very high chance of surviving until very late times if the lifetime, tau _{0}^{F}, of the metastable false vacuum state is much shorter, than the duration of the inflation process. Our analysis shows that the instability of the electroweak vacuum does not have to result in the tragic fate of our Universe leading to its death.

Cosmological \u201cconstant\u201d in a universe born in the metastable false vacuum state

The cosmological constant varLambda is a measure of the energy density of the vacuum. Therefore properties of the energy of the system in the metastable vacuum state reflect properties of varLambda = varLambda (t). We analyze properties of the energy, E(t), of a general quantum system in the metastable state in various phases of the decay process: In the exponential phase, in the transition phase between the exponential decay and the later phase, where decay law as a function of time t is in the form of powers of 1/t, and also in this last phase. We found that this energy having an approximate value resulting from the Weisskopf–Wigner theory in the exponential decay phase is reduced very fast in the transition phase to its asymptotic value E(t) simeq E_{min} + alpha _{2}/t^{2}+ldots in the late last phase of the decay process. (Here E_{min} is the minimal energy of the system). This quantum mechanism reduces the energy of the system in the unstable state by a dozen or even several dozen orders or more. We show that if to assume that a universe was born in metastable false vacuum state then according to this quantum mechanism the cosmological constant varLambda can have a very great value resulting from the quantum field theory calculations in the early universe in the inflationary era, varLambda simeq varLambda _{qft}, and then it can later be quickly reduced to the very, very small values.

Nonlinear dynamics of the cold atom analog false vacuum

We investigate the nonlinear dynamics of cold atom systems that can in princi- ple 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 con- densate (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-wavelength modes driven by the time-dependent coupling. These modes threaten to destabilize the analog false vacuum. Here, we employ numerical simulations of the coupled Gross-Pitaevski equa- tions (GPEs) to determine the non-linear evolution of these linearly unstable modes. We find that unless a physical mechanism modifies the GPE on short length scales, the analog false vacuum is indeed destabilized. We briefly discuss various physically expected correc- tions to the GPEs that may act to remove the exponentially unstable modes. To investigate the resulting dynamics in cases where such a removal mechanism exists, we implement a hard UV cutoff that excludes the unstable modes as a simple model for these corrections. We use this to study the range of phenomena arising from such a system. In particular, we show that by modulating the strength of the time-dependent coupling, it is possible to observe the crossover between a second and first order phase transition out of the false vacuum.

Metastable vacuum decay in center-stabilized Yang-Mills theory at largeN

We calculate the rate of the decay of a metastable vacuum state in $SU(N)$ gauge theory on ${\mathbb R}^3 \times {\mathbb S}^1$ space with a double trace deformation suggested by \"Unsal and Yaffe. The derived analytical expression for the exponential factor in the decay rate, including the dependence on the parameter $\theta$, gives the exact behavior in the leading power of $N$ in the limit of large $N$ and provides a better approximation than a recently found in the literature numerical result.

Metastable vacuum decay and θ dependence in gauge theory. Deformed QCD as a toy model

We study a number of different ingredients related to the θ dependence, metastable excited vacuum states and other related subjects using a simplified version of QCD, the so-called “deformed QCD”. This model is a weakly coupled gauge theory, which, however, preserves all the relevant essential elements allowing us to study hard and nontrivial features which are known to be present in real strongly coupled QCD. Our main focus in this work is to test the ideas related to the metastable vacuum states (which are known to be present in strongly coupled QCD in large N limit) in a theoretically controllable manner using the “deformed QCD” as a toy model. We explicitly show how the metastable states emerge in the system, why their lifetime is large, and why these metastable states must be present in the system for the self-consistency of the entire picture of the QCD vacuum. We also speculate on possible relevance of the metastable vacuum states in explanation of the violation of local P and CP symmetries in heavy ion collisions.

Bubble Collision in Curved Spacetime

We study vacuum bubble collisions in curved spacetime, in which vacuum bubbles were nucleated in the initial metastable vacuum state by quantum tunneling. The bubbles materialize randomly at different times and then start to grow. It is known that the percolation by true vacuum bubbles is not possible due to the exponential expansion of the space among the bubbles. In this paper, we consider two bubbles of the same size with a preferred axis and assume that two bubbles form very near each other to collide. The two bubbles have the same field value. When the bubbles collide, the collided region oscillates back-and-forth and then the collided region eventually decays and disappears. We discuss radiation and gravitational wave resulting from the collision of two bubbles.

Age-dependent decay in the landscape

The picture of the 'multiverse' arising in diverse cosmological scenarios involves transitions between metastable vacuum states. It was pointed out by Krauss and Dent that the transition rates decrease at very late times, leading to a dependence of the transition probability between vacua on the age of each vacuum region. I investigate the implications of this non-Markovian, age-dependent decay on the global structure of the spacetime in landscape scenarios. I show that the fractal dimension of the eternally inflating domain is precisely equal to 3, instead of being slightly below 3, which is the case in scenarios with purely Markovian, age-independent decay. I develop a complete description of a non-Markovian landscape in terms of a nonlocal master equation. Using this description I demonstrate by an explicit calculation that, under some technical assumptions about the landscape, the probabilistic predictions of our position in the landscape are essentially unchanged, regardless of the measure used to extract these predictions. I briefly discuss the physical plausibility of realizing non-Markovian vacuum decay in cosmology in view of the possible decoherence of the metastable quantum state.

OSCILLONS IN SCALAR FIELD THEORIES: APPLICATIONS IN HIGHER DIMENSIONS AND INFLATION

The basic properties of oscillons — localized, long-lived, time-dependent scalar field configurations — are briefly reviewed, including recent results demonstrating how their existence depends on the dimensionality of space–time. Their role on the dynamics of phase transitions is discussed, and it is shown that oscillons may greatly accelerate the decay of metastable vacuum states. This mechanism for vacuum decay — resonant nucleation — is then applied to cosmological inflation. A new inflationary model is proposed which terminates with fast bubble nucleation.

The Vacuum as Ether in the Last Century

In this paper we review the evolution of the concept of “vacuum” according to different theories formulated in the last century, like Quantum Mechanics, Quantum Electrodynamics, Quantum Chromodynamics in Particle Physics and Cosmology. In all these theories a metastable vacuum state is considered which transforms from one state to another according to the energy taken into consideration. It is a “fluid” made up by matter and radiation present in the whole Universe, which may be identified with a modern definition of ether

Kinetic equation for tachyons

The tachyonic regime of the quantum fluctuations of a self-interacting scalar field around its vacuum mean value is studied within a kinetic approach. We derive a quantum kinetic equation which determines the time evolution of the momentum distribution function of produced tachyonic modes and includes memory effects. The back-reaction of the quantum fluctuations on the vacuum mean field is taken into account, while their interaction is neglected. We show that the tachyonic modes do not correspond to real particles and contribute to the decay rate of the metastable vacuum state.

Vacuum decay in quantum field theory

We study the contribution to vacuum decay in field theory due to the interaction between the long- and short-wavelength modes of the field. The field model considered consists of a scalar field of mass M with a cubic term in the potential. The dynamics of the long-wavelength modes becomes diffusive in this interaction. The diffusive behavior is described by the reduced Wigner function that characterizes the state of the long-wavelength modes. This function is obtained from the whole Wigner function by integration of the degrees of freedom of the short-wavelength modes. The dynamical equation for the reduced Wigner function becomes a kind of Fokker-Planck equation which is solved with suitable boundary conditions enforcing an initial metastable vacuum state trapped in the potential well. As a result a finite activation rate is found, even at zero temperature, for the formation of true vacuum bubbles of size ${M}^{\ensuremath{-}1}.$ This effect makes a substantial contribution to the total decay rate.

Dynamics of metastable vacua in the early universe

We study the question whether a possible metastable vacuum state is actually populated in a phase transition in the early universe, as is usually assumed in the discussion of vacuum stability bounds e.g. for Standard Model parameters. A phenomenological (3+1)-dimensional Langevin equation is solved numerically for a toy model with a potential motivated by the finite temperature 1-loop effective potential of the Standard Model including additional non-renormalizable operators from an effective theory for physics beyond the Standard Model and a time dependent temperature. It turns out that whether the metastable vacuum is populated depends critically on the value of the phenomenological parameter η for small scalar couplings. For large enough scalar couplings and with our specific form of the non-renormalizable operators the system (governed by the Langevin equation) always ends up in the metastable minimum.

Tools for tunneling from metastable vacua

If the universe is trapped and cooled in a metastable false vacuum state, that state will eventually decay by bubble nucleation and expansion. For example, many extensions of the standard model incorporate new scalar fields $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\varphi}}$ whose potential has a local minimum at $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\varphi}}=0$ but a global minimum elsewhere, to which the vacuum will eventually tunnel. I calculate the lifetime of the false vacuum, and the field profile of the bubble after tunneling, for any potential that is approximately a polynomial of degree $<~4$ near the false vacuum. Essentially exact results are given for a single field; for multiple fields a strict lower bound is placed on the tunneling rate.

Gauge independence of the bubble nucleation rate in theories with radiative symmetry breaking.

In field theories where a metastable false vacuum state arises as a result of radiative corrections, the calculation of the rate of false vacuum decay by bubble nucleation depends on the effective potential and the other functions that appear in the derivative expansion of the effective action. Beginning with the Nielsen identity, we derive a series of identities that govern the gauge dependence of these functions. Using these, we show, to leading nontrivial order, that, even though these functions are individually gauge dependent, one obtains a gauge-independent result for the bubble nucleation rate. Our formal arguments are complemented by explicit calculations for scalar electrodynamics in a class of ${\mathit{R}}_{\ensuremath{\xi}}$ gauges. \textcopyright{} 1996 The American Physical Society.

Catalyzed decay of a false vacuum in four dimensions.

The probability of destruction of a metastable vacuum state by the field of a highly virtual particle with energy $E$ is calculated for a (3+1) dimensional theory in the leading WKB approximation in the thin-wall limit. It is found that the induced nucleation rate of bubbles, capable of expansion, is exponentially small at any energy. The negative exponential power in the rate reaches its maximum at the energy, corresponding to the top of the barrier in the bubble energy, where it is a finite fraction of the same power in the probability of the spontaneous decay of the false vacuum, i.e. at $E=0$.

Metastability in the early Universe.

The possibility, often explored in the literature, that field theories exhibit metastable vacuum states in the background of a hot expanding universe is examined. By studying the finite-temperature effective potential for self-interacting scalar fields and also for scalar fields interacting with fermion fields, the conditions for the existence of a metastable vacuum are derived. The effects of asymmetries on the effective potential as well as of couplings of the scalar field to other fields on the kinetics of the phase transition are examined. Possible applications to electroweak symmetry breaking, the quark-hadron phase transition, and the primordial formation of nontopological solitons are briefly discussed.

THE GLOBAL STRUCTURE OF THE INFLATIONARY UNIVERSE

In this article we give a review of recent results concerning the global structure of the inflationary universe, which have been obtained within stochastic approach to inflation. It is shown in particular that the evolution of the universe in the chaotic inflation scenario has no end and may have no beginning. In this scenario the major part of the physical volume of the universe always remains in the inflationary phase. During inflation the universe becomes divided into many exponentially large domains, inside which all possible metastable vacuum states and all possible types of compactification compatible with inflation are realized.

Eternally Existing Self-Reproducing Inflationary Universe

It is shown that the large-scale quantum fluctuations of the scalar field φ generated in the chaotic inflation scenario lead to an infinite process of self-reproduction of inflationary mini-universes. A model of an eternally existing chaotic inflationary universe is suggested. It is pointed out that whereas the universe locally is very homogeneous as a result of inflation, which occurs at the classical level, the global structure of the universe is determined by quantum effects and is highly non-trivial. The universe consists of exponentially large number of different mini-universes, inside which all possible (metastable) vacuum states and all possible types of compactification are realized. The picture differs crucially from the standard picture of a one-domain universe in a "true" vacuum state. Our results may serve as a justification of the anthropic principle in the inflationary cosmology. These results may have important implications for the elementary particle theory as well. Namely, since all possible types of mini-universes, in which inflation may occur, should exist in our universe, there is no need to insist (as it is usually done) that in realistic theories the vacuum state of our type should be the only possible one or the best one.

ETERNAL CHAOTIC INFLATION

It is shown that the evolution of the universe in the chaotic inflation scenario has no end and may have no beginning. According to this scenario, the universe consists of an exponentially large number of different mini-universes inside which all possible metastable vacuum states and all possible types of compactifications are realized.