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 arbitrarily small volumes. Casimir energy is a popular candidate for a quantum effect which can ensure this, but [because it violates energy conditions] there is a danger that it could lead to non-perturbative instabilities in string theory. We make a simple proposal for the initial conditions of a bubble universe, and show that our proposal ensures that the system is non-perturbatively stable. Thus, low-entropy conditions can be established at the beginning of a bubble universe without violating the Second Law of thermodynamics and without leading to instability in string theory. These conditions are inherited from the ambient spacetime.
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.
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 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 consider bubble collisions in single scalar field theories with multiple vacua. Recent work has argued that at sufficiently high impact velocities, collisions between such bubble vacua are governed by 'free passage' dynamics in which field interactions can be ignored during the collision, providing a systematic process for populating local minima without quantum nucleation. We focus on the time period that follows the bubble collision and provide evidence that, for certain potentials, interactions can drive significant deviations from the free-passage bubble profile, thwarting the productio…
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 …
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 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…
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 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…
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.
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 …
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…
We discuss models in which vacua other than our own can be directly observed in the present universe. Models with density-dependent vacuum structure can give rise to `non-lethal'-vacua: vacua with lower energy-density than our vacuum, but only in regions with finite Standard Model densities. These models provide an explicit example of a bubble which is confined to a finite region of space and produces potentially detectable signatures, unlike standard Coleman tunneling events where bubbles expand at the speed of light and are never directly observable. We study the expansion and contraction of…
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…
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…
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…
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…
A ``bubble universe'' nucleating in an eternally inflating false vacuum will experience, in the course of its expansion, collisions with an infinite number of other bubbles. In an idealized model, we calculate the rate of collisions around an observer inside a given reference bubble. We show that the collision rate violates both the homogeneity and the isotropy of the bubble universe. Each bubble has a center which can be related to ``the beginning of inflation'' in the parent false vacuum, and any observer not at the center will see an anisotropic bubble collision rate that peaks in the outwa…
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. When in this scenario our bubble universe collides with other ones like it, the collision geometry is constrained by the reduced symmetry of the tunneling instanton. While the regions affected by such bubble collisions still appear (to leading order) as disks in an observer's sky, the cent…
We consider five dimensional deSitter spacetimes with a deficit angle due to the presence of a closed 2-brane and identify one dimension as an extra dimension. From the four dimensional viewpoint we can see that the spacetime has a structure similar to a Kaluza-Klein bubble of nothing, that is, four dimensional spacetime ends at the 2-brane. Since a spatial section of the full deSitter spacetime has the topology of a sphere, the boundary surface surrounds the remaining four dimensional spacetime, and can be considered as the celestial sphere. After the spacetime is created from nothing via an …
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.
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…
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 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…
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 …
In this paper we construct a stringy embedding of the dark bubble model of an expanding 4D cosmology with the help of branes rotating in extra dimensions. The universe rides a bubble which has nucleated in an unstable higher dimensional background. Our construction is therefore a string theoretical realization of Vilenkin's quantum cosmology. While the cosmological constant vanishes at lowest order, loop corrections predicted by the Weak Gravity Conjecture can induce a phenomenologically viable value. The model predicts the existence of large extra dimensions compatible with observational cons…
Growing amount of data show evidence for statistical and apparent physical association between low-redshift galaxies and high-redshift quasi-stellar objects, suggesting noncosmological origin of their redshift and failure of classical quasar explanation. Here we find an analytical solution of Einstein equations describing bubbles made from axions with periodic interaction potential. Such particles are currently considered as one of the leading dark matter candidate. The bubble interior has equal gravitational potential and, hence, photons emitted from the interior possess identical gravitation…
Cosmic bubble collisions provide an important possible observational window on the dynamics of eternal inflation. In eternal inflation, our observable universe is contained in one of many bubbles formed from an inflating metastable vacuum. The collision between bubbles can leave a detectable imprint on the cosmic microwave background radiation. Although phenomenological models of the observational signature have been proposed, to make the theory fully predictive one must determine the bubble collision spacetime, and thus the cosmological observables, from a scalar field theory giving rise to e…
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…
This is the third paper in a series establishing a quantitative relation between inflationary scalar field potential landscapes and the relic perturbations left by the collision between bubbles produced during eternal inflation. We introduce a new method for computing cosmological observables from numerical relativity simulations of bubble collisions in one space and one time dimension. This method tiles comoving hypersurfaces with locally-perturbed Friedmann-Robertson-Walker coordinate patches. The method extends previous work, which was limited to the spacetime region just inside the future …
Recent developments in cosmology suggest that much of the universe is in a state of explosive, accelerated expansion, called inflation. We live in a "bubble" where inflation has ended, and other bubbles with diverse properties are constantly being formed. Most, if not all, of these bubbles are beyond our cosmic horizon and cannot be directly observed. I discuss the origin of this new worldview, its possible observational tests, and its implications for the beginning and the end of the universe.
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 …
Eternal inflation predicts our observable universe lies within a bubble (or pocket universe) embedded in a volume of inflating space. The interior of the bubble undergoes inflation and standard cosmology, while the bubble walls expand outward and collide with other neighboring bubbles. The collisions provide either an opportunity to make a direct observation of the multiverse or, if they produce unacceptable anisotropy, a threat to inflationary theory. The probability of an observer in our bubble detecting the effects of collisions has an absolute upper bound set by the odds of being in the pa…
We study collisions between pairs of bubbles nucleated in an ambient false vacuum. For the first time, we include the effects of small initial (quantum) fluctuations around the instanton profiles describing the most likely initial bubble profile. Past studies of this problem neglect these fluctuations and work under the assumption that the collisions posess an exact SO(2,1) symmetry. We use three-dimensional lattice simulations to demonstrate that for double-well potentials, small initial perturbations to this symmetry can be amplified as the system evolves. Initially the amplification is well…
To compute the spectrum of bubble collisions seen by an observer in an eternally-inflating multiverse, one must choose a measure over the diverging spacetime volume, including choosing an "initial" hypersurface below which there are no bubble nucleations. Previous calculations focused on the case where the initial hypersurface is pushed arbitrarily deep into the past. Interestingly, the observed spectrum depends on the orientation of the initial hypersurface, however one's ability observe the effect rapidly decreases with the ratio of inflationary Hubble rates inside and outside one's bubble. …
When charged particles collide with a vacuum bubble, they can radiate strong electromagnetic waves due to rapid deceleration. Owing to the energy loss of the particles by this bremsstrahlung radiation, there is a non-negligible damping pressure acting on the bubble wall even when thermal equilibrium is maintained. In the non-relativistic region, this pressure is proportional to the velocity of the wall and could have influenced the bubble dynamics in the early universe.
Stochastic gravitational wave background (SGWB) is a promising tool to probe the very early universe where the standard model of particle physics and cosmology are connected closely. As a possible component of SGWB, gravitational waves (GW) from bubble collisions during the first order cosmological phase transitions deserve comprehensive analyses. In 2017, Ryusuke Jinno and Masahiro Takimoto proposed an elegant analysis approach to derive the analytical expressions of energy spectra of GW from bubble collisions in Minkowski spacetime avoiding large-scale numerical simulations for the first tim…
We study models where the gauge coupling constants, masses, etc are functions of some conserved charge in the universe. We first consider the standard Dirac action, but where the mass and the electromagnetic coupling constant are a function of the charge in the universe and afterwards extend this scalar fields. For Dirac field in the flat space formulation, the formalism is not manifestly Lorentz invariant, however Lorentz invariance can be restored by performing a phase transformation of the Dirac field. In the case where scalar field are considered, there is the new feature that an initial c…
If the potential of a scalar field, Phi, which currently provides the ``dark energy'' of the universe, has a negative minimum -M_0^4, then quantum-mechanical fluctuations could nucleate a bubble of Phi at a negative value of the potential. The bubble would expand at the speed of light. Given that no such bubble enveloped us in the past, we find that any minimum in V(Phi) must be separated from the current Phi value by more than min{1.5M_0, 0.21M_Pl}, where M_Pl is the Planck mass. We also show that vacuum decay renders a cyclic or ekpyrotic universe with M_0^4 > 10^{-10}M_Pl^4, untenable.
Quasi-conformal models are an appealing scenario that can offer naturally a strongly supercooled phase transition and a period of thermal inflation in the early Universe. A crucial aspect for the viability of these models is how the Universe escapes from the supercooled state. One possibility is that thermal inflation phase ends by nucleation and percolation of true vacuum bubbles. This route is not, however, always efficient. In such case another escape mechanism, based on the growth of quantum fluctuations of the scalar field that eventually destabilize the false vacuum, becomes relevant. We…
