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 described with the help of thin-wall approximation. False vacuum bubbles have physical importance: a set of false vacuum bubbles might generate a negative energy bath and it has further theoretical implications.
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 paper, we explore the nucleation of vacuum bubbles in the Brans-Dicke type theory of gravity. In the Euclidean signature, we evaluate the fields at the vacuum bubbles as solutions of the Euler-Lagrange equations of motion as well as the bubble nucleation probabilities by integrating the Euclidean action. We illustrate three possible ways to obtain vacuum bubbles: true vacuum bubbles for ω>-3/2, false vacuum bubbles for ω<-3/2, and false vacuum bubbles for ω>-3/2 when the vacuum energy of the false vacuum in the potential of the Einstein frame is less than that of the true vacuum. After…
Given a scalar field with metastable minima, bubbles nucleate quantum mechanically. When bubbles collide, energy stored in the bubble walls is converted into kinetic energy of the field. This kinetic energy can facilitate the classical nucleation of new bubbles in minima that lie below those of the "parent" bubbles. This process is efficient and classical, and changes the dynamics and statistics of bubble formation in models with multiple vacua, relative to that derived from quantum tunneling.
We study the vacuum decay and the bubble nucleation in the anti-de Sitter black holes. In the bubble nucleation spacetime, the interior and the exterior of the bubble wall are described by two anti-de Sitter black hole spacetimes with different cosmological constants. We calculate the Euclidean action of the bubble nucleation spacetime and give the numerical results of the tunneling rates for different cases. It is shown that the black hole can act as a source of inhomogeneities and catalyze the vacuum decay and the bubble nucleation in the anti-de Sitter spacetime. For the RNAdS black holes, …
First-order cosmological phase transitions are considered in the models with an $O(3)$-symmetric scalar field, in the high temperature limit. It is shown that a global monopole can be produced at the center of a bubble when the bubble is nucleated.
In this work we study vacuum decay and bubble nucleation in models of $f(R)$ higher curvature gravity. Building upon the analysis of Coleman-De Luccia (CDL), we present the formalism to calculate the Euclidean action and the bounce solution for a general $f(R)$ gravity in the thin wall approximation. We calculate the size of the nucleated bubble and the decay exponent for the Starobinsky model and its higher power extensions. We have shown that in the Starobinsky model with a typical potential the nucleated bubble has a larger size in comparison to the CDL bubble and with a lower tunneling rat…
In this work we study the imprints of bubble nucleation on primordial inflationary perturbations. We assume that the bubble is formed via the tunneling of a spectator field from the false vacuum of its potential to its true vacuum. We consider the configuration in which the observable CMB sphere is initially outside of the bubble. As the bubble expands, more and more regions of the exterior false vacuum, including our CMB sphere, fall into the interior of the bubble. The modes which leave the horizon during inflation at the time when the bubble wall collides with the observable CMB sphere are …
The non-perturbative instabilities of hot Kaluza-Klein spacetime are investigated. In addition to the known instability of hot space (the nucleation of 4D black holes) and the known instability of KK space (the nucleation of bubbles of nothing by quantum tunneling), we find two new instabilities: the nucleation of 5D black holes, and the nucleation of bubbles of nothing by thermal fluctuation. These four instabilities are controlled by two Euclidean instantons, with each instanton doing double duty via two inequivalent analytic continuations; thermodynamic instabilities of one are shown to be …
One of the key observables in a gravitational wave power spectrum from a first order phase transition in the early Universe is the mean bubble spacing, which depends on the rate of nucleation of bubbles of the stable phase, as well as the bubble wall speed. When the bubbles expand as deflagrations, it is expected that the heating of the fluid in front of the phase boundary suppresses the nucleation rate. We quantify the effect, showing that it increases the mean bubble separation, and acts to enhance the gravitational wave signal by a factor of up to order 10. The effect is largest for small w…
Our universe may have formed via bubble nucleation in an eternally-inflating background. Furthermore, the background may have a compact dimension--the modulus of which tunnels out of a metastable minimum during bubble nucleation--which subsequently grows to become one of our three large spatial dimensions. Then the reduced symmetry of the background is equivalent to anisotropic initial conditions in our bubble universe. We compute the inflationary spectrum in such a scenario and, as a first step toward understanding the effects of anisotropy, project it onto spherical harmonics. The resulting …
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.
Pair production in a constant electric field is closely analogous to bubble nucleation in a false vacuum. The classical trajectories of the pairs are Lorentz invariant, but it appears that this invariance should be broken by the nucleation process. Here, we use a model detector, consisting of other particles interacting with the pairs, to investigate how pair production is seen by different Lorentzian observers. We focus on the idealized situation where a constant external electric field is present for an infinitely long time, and we consider the in-vacuum state for a charged scalar field that…
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.
We extend our previous analysis of the quantum state during and after $O(4)$-symmetric bubble nucleation to the case including gravitational effects. We find that there exists a simple relationship between the case with and without gravitational effects. In a special case of a conformally coupled scalar field which is massless except on the bubble wall, the state is found to be conformally equivalent to the case without gravity.
This paper suggests a model for a bubble universe using buildable false vacuum bubbles. We study the causal structures of collapsing false vacuum bubbles using double-null simulations. False vacuum bubbles violate the null energy condition and emit negative energy along the outgoing direction through semi-classical effects. If there are a few collapsing false vacuum bubbles and they emit negative energy to a certain region, then the region can be approximated by a negative energy bath, which means the region is homogeneously filled by negative energy. If a false vacuum bubble is generated in t…
We have recently suggested that tiny black holes can act as nucleation seeds for the decay of the metastable Higgs vacuum. Previous results applied only to the nucleation of thin-wall bubbles, and covered a very small region of parameter space. This paper considers bubbles of arbitrary profile and reaches the same conclusion: black holes seed rapid vacuum decay. Seeded and unseeded nucleation rates are compared, and the gravitational back reaction of the bubbles is taken into account. The evolution of the bubble interior is described for the unseeded nucleation. Results are presented for the r…
We study gravitational-wave production from bubble collisions in a cosmic first-order phase transition, focusing on the possibility of model separation by the bubble nucleation rate dependence of the resulting gravitational-wave spectrum. By using the method of relating the spectrum with the two-point correlator of the energy-momentum tensor $\left< T(x)T(y) \right>$, we first write down analytic expressions for the spectrum with a Gaussian correction to the commonly used nucleation rate, $Γ\propto e^{βt}\rightarrow e^{βt-γ^2t^2}$, under the thin-wall and envelope approximations. Then we quant…
Using the multi-dimensional wave function formalism, we investigate the quantum state of a scalar field inside a true vacuum bubble nucleated through false vacuum decay in flat spacetime. We developed a formalism which allows us a mode-by-mode analysis. To demonstrate its advantage, we describe in detail the evolution of the quantum state during the tunneling process in terms of individual mode functions and interpret the result in the language of particle creation. The spectrum of the created particles is examined based on quantum field theory in the Milne universe.
We study the false vacuum decay and bubble nucleation in the presence of a cosmic string in dS spacetime. A cosmic string induces a deficit angle in spacetime around itself so the nucleated bubble has the shape of a rugby ball. Working in thin wall approximation and using the junction conditions we study the dynamics of the bubble wall and calculate the Euclidean action. An interesting feature in our analysis is that the tension of the string is screened by the bubble such that an observer inside the bubble measures a different value of the tension than an outside observer. We show that the st…
The O(4)-symmetric regular instanton solutions are studied within the framework of the Eddington-inspired-Born-Infeld gravity (EiBI). We find that the behavior of the solution would deviate from that in Einstein gravity when the kinetic energy of the scalar field is sufficiently large. The tunneling probability is calculated numerically in different parameter space. We find that the tunneling probability would increase with the Born-Infeld coupling constant, which is assumed to be positive in this paper. Furthermore, we discover a neck feature in the physical instanton solutions when the kinet…
False vacuum decay in quantum mechanical first order phase transitions is a phenomenon with wide implications in cosmology, and presents interesting theoretical challenges. In the standard approach, it is assumed that false vacuum decay proceeds through the formation of bubbles that nucleate at random positions in spacetime and subsequently expand. In this paper we investigate the presence of correlations between bubble nucleation sites using a recently proposed semi-classical stochastic description of vacuum decay. This procedure samples vacuum fluctuations, which are then evolved using class…
We discuss the computation of the quantum effective action of strongly interacting field theories using holographic duality, and its use to determine quasi-equilibrium parameters of first order phase transitions relevant for gravitational wave production. A particularly simple holographic model is introduced, containing only the metric and a free massive scalar field. Despite the simplicity, the model contains a rich phase diagram, including first order phase transitions at non-zero temperature, due to various multi-trace deformations. We obtain the leading terms in the effective action from h…
The Euclidean action is calculated in the thin-wall approximation for a first-order vacuum phase transition in which the bubble appears symmetrically around either a global monopole or a gauge cosmic string. The bubble is assumed to be much larger than the core size of the monopole or string. In both cases the value of the Euclidean action is shown to be reduced below the $O(4)$ symmetric action value, indicating that the topological defects act as effective nucleation sites for vacuum decay.
