We consider the model of a false vacuum bubble with a thin wall where the surface energy density is composed of two different components, "domain-wall" type and "dust" type, with opposite signs. We find stably oscillating solutions, which we call "breathing bubbles". By decay to a lower mass state, such a breathing bubble could become either i) a child universe or ii) a bubble that "eats up" the original universe, depending on the sign of the surface energy of the "domain-wall" component. We also discuss the effect of the finite-thickness corrections to the thin-wall approximation and possible origins of the energy contents of our model.
We discuss a possible scenario to induce a bubble universe using buildable bubbles. First, we observe that if there is no violation of the null energy condition, all bubbles are buildable and do not have inflation if their initial conditions are assigned along the in-going null surface in an almost flat background. However, if the null energy condition is sufficiently violated, then the generation of a bubble universe is possible. Second, the author will observe that a sufficient violation of the null energy condition may be possible using a buildable bubble due to the Hawking radiation of a d…
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…
We show that the bubbles $S^2\times S^2$can be created from vacuum fluctuation in certain De Sitter universe, so the space-time foam-like structure might really be constructed from bubbles of $S^2\times S^2$ in the very early inflating phase of our universe. But whether such foam-like structure persisted during the later evolution of the universe is a problem unsolved now.
We consider a cosmological model in which our Universe is a spherically symmetric bubble wall in 5-dimensional anti-de Sitter spacetime. We argue that the bubble on which we live will undergo collisions with other similar bubbles and estimate the spectrum of such collisions. The collision rate is found to be independent of the age of our Universe. Collisions with small bubbles provide an experimental signature of this scenario, while collisions with larger bubbles would be catastrophic.
The influence of the shape of scalar field potential on the outcome of vacuum decay in de Sitter universe is studied. Sufficient condition for vacuum decay via bubble formation, described by Coleman - de Luccia instanton, is revisited and necessary condition is found. Both conditions require that the curvature of the potential is greater than 4 $\times$ (Hubble constant)$^2$, but while the sufficient condition states that this inequality is to be valid at the top of the barrier, the necessary condition requires that it holds at least somewhere throughout the barrier. The conditions leave a 'gr…
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 investigate the bubble nucleation in five dimensional spacetime catalyzed by quintessence. We especially focus on decay of a metastable Minkowski vacuum to an anti-de Sitter vacuum and study dynamics of the bubble on which four dimensional expanding universe is realized. We also discuss the trans-Planckian censorship conjecture and impose a constraint on the parameter space of the catalysis. As an application of this model, we propose an inflation mechanism and an origin of the dark energy in the context of quintessence in five dimensions.
An introduction to models of open universes originating from bubbles, including a summary of recent theoretical results for the power spectrum. To appear in the proceedings of the XXXIth Moriond meeting, "Microwave Background Anisotropies."
The "bubble universes" of Coleman and De Luccia play a crucial role in string cosmology. Since our own Universe is supposed to be of this kind, bubble cosmology should supply definite answers to the long-standing questions regarding cosmological initial conditions. In particular, it must explain how an initial singularity is avoided, and also how the initial conditions for Inflation were established. We argue that the simplest non-anthropic approach to these problems involves a requirement that the spatial sections defined by distinguished bubble observers should not be allowed to have arbitra…
We show that particle production during the expansion of bubbles of true vacuum in the sea of false vacuum is possible and calculate the resulting rate. As a result the nucleated bubbles cannot expand due to the transfer of false vacuum energy to the created particles inside the bubbles. Therefore all the inflationary models dealing with the nucleation and expansion of the bubbles (including extended inflation) may not be viable.
We argue a scenario motivated by the context of string landscape, where our universe is produced by a new vacuum bubble embedded in an old bubble and these bubble universes have not only different cosmological constants, but also their own different gravitational constants. We study these effects on the primordial curvature perturbations. In order to construct a model of varying gravitational constants, we use the Jordan-Brans-Dicke (JBD) theory where different expectation values of scalar fields produce difference of constants. In this system, we investigate the nucleation of bubble universe …
We consider an alternative scenario of inflation which can account for a spatially open universe. It is similar to the old inflation in which the bubble nucleation occurs in the sea of false vacuum, but differs from it in that the second slow rollover inflation occurs inside a nucleated bubble. Hence our observable universe is entirely contained in one nucleated bubble. The significance of the scenario is that apart from a variance due to model parameters it gives us a definite prediction on the spectrum of the primordial density perturbations, hence is observationally testable. Here we invest…
Faddeev and Jackiw's method for constrained systems is used to derive a gauge invariant formulation of cosmological perturbations in the one bubble inflationary universe. For scalar perturbations in a flat universe, reduction of the action to the one with a single physical degree of freedom has been derived in the literature. A straightforward generalization of it to the case of an open universe is possible but it is not adequate for quantizing perturbations in the one bubble universe, because of the lack of Cauchy surfaces inside the bubble. Therefore we perform the reduction of the action ou…
This is a very informal report that gives further details on the evidence for a bubble universe based on an anomaly in the angular distribution of quasar magnitudes that was presented in a short paper in arXiv:1202.4433. This report addresses some concerns of two reviewers. It is meant to be read in conjunction with 1202.4433. There is very little overlap between the two articles. This extended discussion is, by necessity, somewhat more technical in nature. I am grateful for the reviewers' comments that forced me to understand these issues more thoroughly.
We assess the effects of a collision between two vacuum bubbles in the thin-wall limit. After describing the outcome of a generic collision possessing the expected hyperbolic symmetry, we focus on collisions experienced by a bubble containing positive vacuum energy, which could in principle contain our observable universe. We provide criteria governing whether the post-collision domain wall accelerates towards or away from this "observation" bubble, and discuss the implications for observers located at various positions inside of the bubble. Then, we identify the class of solutions which have …
We comment on the global structure of the spacetime that results from the collision of two bubbles filled with AdS space produced from the decay of a false vacuum through quantum tunnelling.
We study the proposal that a de Sitter (dS) universe with an Anti-de Sitter (AdS) bubble can be replaced by a dS universe with a boundary CFT. To explore this duality, we consider incident gravitons coming from the dS universe through the bubble wall into the AdS bubble in the original picture. In the dual picture, this process has to be identified with the absorption of gravitons by CFT matter. We have obtained a general formula for the absorption probability in general $d+1$ spacetime dimensions. The result shows the different behavior depending on whether spacetime dimensions are even or od…
Bubble universes and traversable wormholes in general relativity can be realized as two sides of the same concept. To exemplify, we find, display, and study in a unified manner a Minkowski-Minkowski closed universe and a Minkowski-Minkowski traversable wormhole. By joining two 3-dimensional flat balls along a thin shell two-sphere of matter, i.e., a spherical domain wall, into a single spacetime one gets a Minkowski-Minkowski static closed universe, i.e., a bubble universe. By joining two 3-dimensional complements of flat balls along a thin shell two-sphere of matter, i.e., a spherical throat,…
The nucleation and evolution of bubbles are investigated in the model of an $O(3)$-symmetric scalar field coupled to gravity in the high temperature limit. It is shown that, in addition to the well-known bubble of which the inside region is true vacuum, there exists another decay channel at high temperature which is described by a new solution such that a false vacuum region like a global monopole remains at the center of a bubble. The value of the Euclidean action of this bubble is higher than that of the ordinary bubble; however, the production rate of it can be considerable for a certain ra…
We evaluate the possibility of observable effects arising from collisions between vacuum bubbles in a universe undergoing false-vacuum eternal inflation. Contrary to conventional wisdom, we find that under certain assumptions most positions inside a bubble should have access to a large number of collision events. We calculate the expected number and angular size distribution of such collisions on an observer's "sky," finding that for typical observers the distribution is anisotropic and includes many bubbles, each of which will affect the majority of the observer's sky. After a qualitative dis…
We investigate the decay of metastable de Sitter, Minkowski and anti-de Sitter vacua catalyzed by a black hole and a cloud of strings. We apply the method to the creation of the four dimensional bubble universe in the five dimensional anti-de Sitter spacetime recently proposed by Banerjee, Danielsson, Dibitetto, Giri and Schillo. We study the bounce action for the creation and find that the bubble with very small cosmological constant, of order $Λ^{(4)}/M^2_4 \sim 10^{-120}$, is favored by the catalysis by assuming appropriate mass scales of the black hole and the cloud of strings to reproduce…
We study the effect of a bubble wall on the entanglement entropy of a free massive scalar field between two causally disconnected open charts in de Sitter space. We assume there is a delta-functional wall between the open charts. This can be thought of as a model of pair creation of bubble universes in de Sitter space. We first derive the Euclidean vacuum mode functions of the scalar field in the presence of the wall in the coordinates that respect the open charts. We then derive the Bogoliubov transformation between the Euclidean vacuum and the open chart vacua that makes the reduced density …
We compute the cosmological perturbations generated in the colliding bubble braneworld universe in which bubbles filled with five-dimensional anti-de Sitter space (AdS5)expanding within a five dimensional de Sitter space (dS5) or Minkowski space (M5) collide to form a (3+1) dimensional local brane on which the cosmology is virtually identical to that of the Randall-Sundrum model. The perturbation calculation presented here is valid to linear order but treats the fluctuations of the expanding bubbles as (3+1) dimensional fields localized on the bubble wall. We find that for bubbles expanding in…
The stability of our vacuum is analyzed and several aspects concerning this question are reviewed. 1) In the standard Glashow-Weinberg-Salam (GWS) model we review the instability towards the formation of a bubble of lower energy density and how the rate of such bubble formation process compares with the age of the Universe for the known values of the GWS model. 2) We also review the recent work by one of us (E.I.G) concerning the vacuum instability question in the context of a model that solves the cosmological constant problem. It turns out that in such model the same physics that solves the …
We revisit the issue of the stability in the Dvali-Gabadadze-Porrati model, by considering the nucleation of bubbles of the conventional branch within the self-accelerating branch. We construct an instanton describing this process in the thin wall approximation. On one side of the bubble wall, the bulk consists of the exterior of the brane while on the other side it is the interior. The solution requires the presence of a 2-brane (the bubble wall) which induces the transition. However, we show that this instanton cannot be realized as the thin wall limit of any smooth solution. Once the bubble…
The primordial Universe might be highly inhomogeneous. We perform the 3+1D Numerical Relativity simulation for the evolution of scalar field in an initial inhomogeneous expanding Universe, and investigate how it populates the landscape with both de Sitter (dS) and AdS vacua. The simulation results show that eventually either the field in different region separates into different vacua, so that the expanding dS or AdS bubbles (the bubble wall is expanding but the spacetime inside AdS bubbles is contracting) come into being with clear bounderies, or overall region is dS expanding with a few smal…
Quasars provide our farthest-reaching view of the Universe. The Sloan Survey now contains over 100,000 quasar candidates. A careful look at the angular distribution of quasar magnitudes shows a surprising intensity enhancement with a "bulls eye" pattern toward (alpha,delta) ~ (195°, 0°) for all wavelengths from UV through infrared. The angular pattern and size of the enhancement is very similar for all wavelengths, which is inconsistent with a Doppler shift due to a large peculiar velocity toward that direction. The shift is also too large to explain as a systematic error in the quasar magnitu…
The interface between a big bubble of true AdS$_D$ vacuum expanding inside a false AdS$_D$ vacuum is a model of an inflating $D-1$ dimensional universe. It looks like an interesting setup to study fundamentals of inflation. A recent computation shows that the prediction of this model for the wavefunction of the universe disagrees with that of Hartle and Hawking. We show that this discrepancy is because the effective $D-1$ dimensional description of the model is spin-$0$ (Nordström) gravity rather than spin-2 (Einstein) gravity.
We apply the principles of quantum mechanics and quantum cosmology to predict probabilities for our local observations of a universe undergoing false vacuum eternal inflation. At a sufficiently fine-grained level, histories of the universe describe a mosaic of bubble universes separated by inflationary regions. We show that predictions for local observations can be obtained directly from sets of much coarser grained histories which only follow a single bubble. These coarse-grained histories contain neither information about our unobservable location nor about the unobservable large-scale struc…
Observing the relics of collisions between bubble universes would provide direct evidence for the existence of an eternally inflating Multiverse; the non-observation of such events can also provide important constraints on inflationary physics. Realizing these prospects requires quantitative predictions for observables from the properties of the possible scalar field Lagrangians underlying eternal inflation. Building on previous work, we establish this connection in detail. We perform a fully relativistic numerical study of the phenomenology of bubble collisions in models with a single scalar …
The spectrum of cosmological perturbations in the context of the one-bubble open inflation model is discussed, taking into account fluctuations of the metric. We find that, quite generically,thin wall single field models have no supercurvature modes. However, single field models with supercurvature modes do exist. In these models the density parameter $Ω$ becomes a random variable taking a range of values inside of each bubble. We also show that the model dependence of the continuous spectrum for both scalar and tensor-type perturbations is small as long as the kinetic energy density of the ba…
The unexpected dimness of Type Ia supernovae at redshifts z >~ 1 has over the past 7 years been seen as an indication that the expansion of the universe is accelerating. A new model cosmology, the "fractal bubble model", has been proposed by one of us [gr-qc/0503099], based on the idea that our observed universe resides in an underdense bubble remnant from a primordial epoch of cosmic inflation, together with a new solution for averaging in an inhomogeneous universe. Although there is no cosmic acceleration, it is claimed that the luminosity distance of type Ia supernovae data will nonetheless…
In this letter we discuss cosmological first order phase transitions with de Sitter bubbles nucleating on (inhomogeneous) matter backgrounds. The de Sitter bubble can be a toy model for an inflationary phase of universes like our own. Using the thin wall approximation and the Israel junction method we trace the classical evolution of the formed bubbles within a compound model. We first address homogeneous ambient space (FRW model) and already find that bubbles nucleated in a dust dominated background cannot expand. For an inhomogeneous dust background (LTB model) we describe cases with at leas…
In the eternally inflating background, the bubbles with AdS vacua will crunch. However, this crunch might be followed by a bounce. It is generally thought that the bubble universe may be cyclic, which will go through a sequence of AdS crunches, until the field inside bubble finally lands at a dS minimum. However, we show that due to the amplification of field fluctuation, the bubble universe going through AdS cycles will inevitably fragment within two or three cycles. We discuss its implication to the eternal inflation scenario.
Much work has been devoted to the phenomenology and cosmology of the so-called braneworld universe, where our (3+1)-dimensional universe lies on a brane surrounded by a (4+1)-dimensional bulk spacetime that is essentially empty except for a negative cosmological constant and the various modes associated with gravity. For such a braneworld cosmology, the difficulty of justifying some preferred initial conditions inevitably arises. The various proposals for inflation restricted to the brane only partially explain the homogeneity and isotropy of the resulting braneworld universe because the homog…
It is widely believed that the standard model is a low energy effective theory which may have higher dimensional non-renormalizable operators. The existence of these new operators can lead to interesting dynamics for the evolution of the universe, including the appearance of new vacuum states. If the universe today exists in a false vacuum, there will be a non-zero probability to tunnel to the true vacuum state of the universe. Should this transition occur elsewhere in the universe, bubbles of true vacuum will nucleate and expand outwards. Bubbles that nucleate in the hot dense plasma of the e…
We point out a possible generation mechanism of non-Gaussian bubbles in the sky due to bubble nucleation in the early universe. We consider a curvaton scenario for inflation and assume that the curvaton field phi, whose energy density is subdominant during inflation but which is responsible for the curvature perturbation of the universe, is coupled to another field sigma which undergoes false vacuum decay through quantum tunneling. For this model, we compute the skewness of the curvaton fluctuations due to its interaction with sigma during tunneling, that is, on the background of an instanton …
It is intriguing to consider the possibility that the Big Bang of the standard (3+1) dimensional cosmology originated from the collision of two branes within a higher dimensional spacetime, leading to the production of a large amount of entropy. In this paper we study, subject to certain well-defined assumptions, under what conditions such a collision leads to an expanding universe. We assume the absence of novel physics, so that ordinary (4+1) -dimensional Einstein gravity remains a valid approximation. It is necessary that the fifth dimension not become degenerate at the moment of collision.…
We propose an alternative inflationary universe scenario in the context of Randall-Sundrum braneworld cosmology. In this new scenario the existence of extra-dimension(s) plays an essential role. First, the brane universe is initially in the inflationary phase driven by the effective cosmological constant induced by small mismatch between the vacuum energy in the 5-dimensional bulk and the brane tension. This mismatch arises since the bulk is initially in a false vacuum. Then, the false vacuum decay occurs, nucleating a true vacuum bubble with negative energy inside the bulk. The nucleated bubb…
The theory of eternal inflation in an inflaton potential with multiple vacua predicts that our universe is one of many bubble universes nucleating and growing inside an ever-expanding false vacuum. The collision of our bubble with another could provide an important observational signature to test this scenario. We develop and implement an algorithm for accurately computing the cosmological observables arising from bubble collisions directly from the Lagrangian of a single scalar field. We first simulate the collision spacetime by solving Einstein's equations, starting from nucleation and endin…
An interesting idea is that the universe could be spontaneously created from nothing, but no rigorous proof has been given. In this paper, we present such a proof based on the analytic solutions of the Wheeler-DeWitt equation (WDWE). Explicit solutions of the WDWE for the special operator ordering factor p=-2 (or 4) show that, once a small true vacuum bubble is created by quantum fluctuations of the metastable false vacuum, it can expand exponentially no matter whether the bubble is closed, flat or open. The exponential expansion will end when the bubble becomes large and thus the early univer…
An appealing theory is that our current patch of universe was born as a nucleation bubble from a phase of false vacuum eternal inflation. We search for evidence for this theory by looking for the signal imprinted on the CMB that is generated when another bubble "universe" collides with our own. We create an efficient and optimal estimator for the signal in the WMAP 7-year data. We find no detectable signal, and constrain the amplitude, a, of the initial curvature perturbation that would be generated by a collision: -4.66 \times 10^{-8} < a (\sin{\thetabubble})^{4/3} < 4.73 \times 10^{-8} [Mpc^…
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.
In the context of the open inflationary universe, we calculate the amplitude of quantum fluctuations which deform the bubble shape. These give rise to scalar field fluctuations in the open Friedman-Robertson-Walker universe which is contained inside the bubble. One can transform to a new gauge in which matter looks perfectly smooth, and then the perturbations behave as tensor modes (gravitational waves of very long wavelength). For $(1-Ω)<<1$, where $Ω$ is the density parameter, the microwave temperature anisotropies produced by these modes are of order $δT/T\sim H(R_0μl)^{-1/2} (1-Ω)^{l/2}$. …
Current theories of the origin of the Universe, including string theory, predict the existence of a multiverse containing many bubble universes. These bubble universes will generically collide, and collisions with ours produce cosmic wakes that enter our Hubble volume, appear as unusually symmetric disks in the cosmic microwave background (CMB) and disturb large scale structure (LSS). There is preliminary observational evidence consistent with one or more of these disturbances on our sky. However, other sources can produce similar features in the CMB temperature map and so additional signals a…
The problem of making predictions in eternally inflating universe that thermalizes by bubble nucleation is considered. A recently introduced regularization procedure is applied to find the probability distribution for the ensemble of thermalized bubbles. The resulting probabilities are shown to be independent of the choice of the time parametrization. This formalism is applied to models of open ``hybrid'' inflation with $Ω<1$. Depending on the parameters of the model, the probability distribution for $Ω$ is found to have a peak either very close to $Ω=1$, or at an intermediate value of $Ω$ in …
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 …
Analog Cosmology in a Quenched Bose-Einstein Condensate Bubble
Louisiana State University（路易斯安那州立大学）；Leibniz Universität Hannover（汉诺威莱布尼茨大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；The Australian National University（澳大利亚国立大学）
Vacuum bubbles may nucleate and expand during the inflationary epoch in the early universe. After inflation ends, the bubbles quickly dissipate their kinetic energy; they come to rest with respect to the Hubble flow and eventually form black holes. The fate of the bubble itself depends on the resulting black hole mass. If the mass is smaller than a certain critical value, the bubble collapses to a singularity. Otherwise, the bubble interior inflates, forming a baby universe, which is connected to the exterior FRW region by a wormhole. A similar black hole formation mechanism operates for spher…
We introduce an effective Lagrangian which describes the classical and semiclassical dynamics of spherically symmetric, self-gravitating objects that may populate the Universe at large and small (Planck) scale. These include wormholes, black holes and inflationary bubbles. We speculate that such objects represent some possible modes of fluctuation in the primordial spacetime foam out of which our universe was born. Several results obtained by different methods are encompassed and reinterpreted by our effective approach. As an example, we discuss: i) the gravitational nucleation coefficient for…
We show that a large class of two-field models of single-bubble open inflation do not lead to infinite open universes, as it was previously thought, but to an ensemble of very large but finite inflating `islands'. The reason is that the quantum tunneling responsible for the nucleation of the bubble does not occur simultaneously along both field directions and equal-time hypersurfaces in the open universe are not synchronized with equal-density or fixed-field hypersurfaces. The most probable tunneling trajectory corresponds to a zero value of the inflaton field; large values, necessary for the …
A new model of the observed universe, using solutions to the full Einstein equations, is developed from the hypothesis that our observable universe is an underdense bubble, with an internally inhomogeneous fractal bubble distribution of bound matter systems, in a spatially flat bulk universe. It is argued on the basis of primordial inflation and resulting structure formation, that the clocks of the isotropic observers in average galaxies coincide with clocks defined by the true surfaces of matter homogeneity of the bulk universe, rather than the comoving clocks at average spatial positions in …
The Raychaudhuri equation for null rays is a powerful tool for finding consistent embeddings of cosmological bubbles into a background spacetime in a way that is largely independent of the matter content. We find that spatially flat or positively curved thin wall bubbles surrounded by a cosmological background must have a Hubble expansion that is either contracting or expanding slower than the background, which are more stringent constraints than those obtained by the usual Israel thin-wall formalism. Similarly, a cosmological bubble surrounded by Schwarzschild space, occasionally used as a si…
