Sugumi Kanno, Jiro Soda
We present exact Coleman-de Luccia (CdL) instantons, which describe vacuum decay from Anti de Sitter (AdS) space, de Sitter (dS) space and Minkowski space to AdS space. We systematically obtain these exact solutions by considering deformation of Hawking-Moss (HM) instantons. We analytically calculate decay rates and discuss a subtlety in the interpretation.
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We present the necessary and sufficient conditions for a Euclidean scale factor to be a solution of the Coleman-De Luccia equations for some analytic potential $V(ϕ)$, with a Lorentzian continuation describing the growth of a bubble of lower-energy vacuum surrounded by higher-energy vacuum. We then give a set of explicit examples that satisfy the conditions and thus are closed-form analytic examples of Coleman-De Luccia geometries.
We reconsidered the Coleman de Luccia solution building an AdS4 bubble expanding into a false flat vacuum. In this construction when junction conditions are imposed we find an upper bound to the radius of the AdS4 and a domain wall whose tension is a function of the minimum of the scalar potential. We prove that this solution is exactly the solution found by Coleman and de Luccia, but in addition there is a new condition that restricts the AdS4 radius and a precise relation between the tension and the minimum of the scalar potential. The applicability of the ADS/CFT correspondence is discussed…
I point out that the usual Coleman-de Luccia analysis of tunnelling via instantons between perturbatively stable minima using the thin-wall approximation misses one of the effects of gravitational backreaction on the on-shell action and hence the decay rate. Once this oversight is corrected, one finds these decay rates are much larger than has been generally appreciated; including the effects of gravity potentials involving barriers which are relatively high and not overly wide result in decays which are quite rapid instead of slow. In the light of these results, it is no longer clear that one…
Coleman-de Luccia processes for AdS to AdS decays in Einstein-scalar theories are studied. Such tunnelling processes are interpreted as vev-driven holographic RG flows of a quantum field theory on de Sitter space-time. These flows do not exist for generic scalar potentials, which is the holographic formulation of the fact that gravity can act to stabilise false AdS vacua. The existence of Coleman-de Luccia tunnelling solutions in a potential with a false AdS vacuum is found to be tied to the existence of exotic RG flows in the same potential. Such flows are solutions where the flow skips possi…
We revisit the famous Coleman-de Luccia formalism for decay of false vacuum in gravitational theory. Since the corresponding wave function is time-independent we argue that its instanton's interpretation as the decay rate probability is problematic. We instead propose that such phenomenon can better be described by the Wheeler-de Witt's wave function. To do so, the Hamilton-Jacobi formalism is employed in the WKB approximation. The scalar and gravitational fields can then be treated as a two-dimensional effective metric. For a particular case of dS-to-dS tunneling, we calculated the wave funct…
Stringy effects on vacuum transitions are shown to include surprisingly large decay rates through very high potential barriers. This simple, yet counter-intuitive result will drastically modify the measure on the landscape of string vacua.
The usual (type A) thin-wall Coleman-de Luccia instanton is made by a bigger-than-half sphere of the false vacuum and a smaller-than-half sphere of the true vacuum. It has a the standard O(4) symmetric negative mode associated with changing the size of false vacuum region. On the other hand, the type B instanton, made by two smaller-than-half spheres, was believed to have lost this negative mode. We argue that such belief is misguided due to an over-restriction on Euclidean path integral. We introduce the idea of a "purely geometric junction" to visualize why such restriction could be removed,…
We derive the rate for transitions between de Sitter vacua by treating the field theory on the static patch as a thermal system. This reproduces the Coleman-De Luccia formalism for calculating the rate, but leads to a modified interpretation of the bounce solution and a different prediction for the evolution of the system after tunneling. The bounce is seen to correspond to a sequence of configurations interpolating between initial and final configurations on either side of the tunneling barrier, all of which are restricted to the static patch. The final configuration, which gives the initial …
JT de Sitter Gravity as a Model of Coleman-de Luccia Tunneling
该研究将JT de Sitter引力的欧几里得解解释为Coleman-de Luccia瞬子，探讨低熵视界衰变过程，并通过量子力学模型验证半经典计算的准确性。
One loop aspects of Coleman de Luccia instantons at small backreaction
本文在小反作用极限下计算Coleman de Luccia瞬子的一圈路径积分贡献，澄清对称性破缺后零模贡献的变化，提出假真空衰变率的引力路径积分公式，并给出研究路径积分相位随参数变化的方案。
Is the Coleman de Luccia action minimum?: AdS/CFT approach
本文利用 AdS/CFT 对应，证明了在特定条件下（AdS背景、真空半径相近、薄壁近似），Coleman de Luccia 作用量是亚稳态 AdS 真空衰变中的最小作用量，从而规避了引力系统中的负模和无界作用量问题。
We study the Coleman-de Luccia (CDL) instanton characterizing the tunneling from a false vacuum to the true vacuum in a semi-classical way in dRGT (deRham-Gabadadze-Tolley) massive gravity theory, and evaluate the dependence of the tunneling rate on the model parameters. It is found that provided with the same physical Hubble parameters for the true vacuum $H_{\rm T}$ and the false vacuum $H_{\rm F}$ as in General Relativity (GR), the thin-wall approximation method implies the same tunneling rate as GR. However, deviations of tunneling rate from GR arise when one goes beyond the thin-wall appr…
This paper presents a simple framework that organizes thin-wall Coleman-De Luccia instantons based on the Euclidean geometries of their original and tunneled vacuum patches. We consider all a priori allowed vacuum pairs (de Sitter or Anti-de Sitter for either patch, Minkowski can be obtained as a limit of either), and $O(4)$-symmetric thin-wall geometries connecting them. For each candidate bounce geometry, either a condition under which a solution to the $O(4)$-invariant equations of motion exists is derived, or the would-be vacuum transition is ruled out. For the parameter regimes in which a…
The Origin and Fate of Rapid Negative Modes in Coleman--De Luccia Tunneling
本文揭示Coleman--De Luccia隧穿中快速振荡负模塔源于单一引力共形扇区，而非多个不稳定性，并在共同规范与调节器下抵消，仅剩单个负模，为计算前因子扫清障碍。
We study the negative modes of gravitational instantons representing vacuum decay in asymptotically flat space-time. We consider two different vacuum decay scenarios: the Coleman-de Luccia $\mathrm{O}(4)$-symmetric bubble, and $\mathrm{O}(3) \times \mathbb{R}$ instantons with a static black hole. In spite of the similarities between the models, we find qualitatively different behaviours. In the $\mathrm{O}(4)$-symmetric case, the number of negative modes is known to be either one or infinite, depending on the sign of the kinetic term in the quadratic action. In contrast, solving the mode equat…
Coleman-de Luccia transitions are spontaneous processes of nucleation of bubbles within metastable gravitational vacua including in their interior a true stable vacuum. From the perspective of lower-dimensional gauged supergravities obtained by truncating Type II and M-theory, these instantonic processes are represented by smooth domain walls featured by de Sitter foliations. These geometries must connect two different AdS vacua in such a way that the wall is defined by an interior and an exterior. We propose a first-order formulation for such radial flows and present two fully backreacted exa…
We investigate the negative modes about Coleman-De Luccia bounces governing vacuum transitions in de Sitter space, with the goal of gaining physical insight into the various anomalous results associated with these that have been reported in the literature. For the case of bounces with radii much less that the horizon distance $H^{-1}$ we find two distinct regimes, distinguished by the magnitude of the bubble nucleation rate $Γ$. If $Γ/H^4 \gg 1$, then the behavior of the modes contributing to the determinant factors in $Γ$ is much as in flat spacetime, and the calculation of $Γ$ goes over smoo…
We study Coleman-de Luccia tunneling in some detail. We show that, for a single scalar field potential with a true and a false vacuum, there are four types of tunneling, depending on the properties of the potential. A general tunneling process involves a combination of thermal (Gibbons-Hawking temperature) fluctuation part way up the barrier followed by quantum tunneling. The thin-wall approximation is a special limit of the case (of only quantum tunneling) where inside the nucleation bubble is the true vacuum while the outside reaches the false vacuum. Hawking-Moss tunneling is the (only ther…
We complete an old argument that causal diamonds in the crunching region of the Lorentzian continuation of a Coleman-Deluccia instanton for transitions out of de Sitter space have finite area, and provide quantum models consistent with the principle of detailed balance, which can mimic the instanton transition probabilities for the cases where this diamond is larger or smaller than the causal patch of de Sitter space. We review arguments that potentials which do not have a positive energy theorem when the lowest de Sitter minimum is shifted to zero, may not correspond to real models of quantum…
We show that gravitational interactions between massless thermal modes and a nucleating Coleman-de Luccia bubble may lead to efficient decoherence and strongly suppress metastable vacuum decay for bubbles that are small compared to the Hubble radius. The vacuum decay rate including gravity and thermal photon interactions has the exponential scaling $Γ\simΓ_{CDL}^{2}$, where $Γ_{CDL}$ is the Coleman-de Luccia decay rate neglecting photon interactions. For the lowest metastable initial state an efficient quantum Zeno effect occurs due to thermal radiation of temperatures as low as the de Sitter …
We investigate the cosmological signatures of instantons mediating tunneling between de Sitter minima. For generic potentials the Coleman-de Luccia instanton does not necessarily exist; when it does not, the instanton which contributes to the decay rate is the trivial constant solution, known as the Hawking-Moss instanton. With the aid of a toy model we interpret this solution and describe the resulting cosmology. In neither the Coleman-de Luccia nor Hawking-Moss case can the resulting cosmology be closed. An observation of significant positive curvature would therefore rule out the possibilit…
We identify infinite classes of potentials for which the Coleman instantons do not exist. For these potentials, the decay of a false vacuum must be described by the new instantons introduced in [7,8].
Beyond Coleman's Instantons
本文研究了在有限作用量条件下，非O(4)对称的奇异瞬子解的可能性，发现存在与O(4)对称解作用量相同的变形解，暗示可能有更低作用量的非对称瞬子解。
We identify an infinite class of unbounded potentials for which the Coleman instantons do not exist in D-dimensional spacetime. For such potentials, the decay of a false vacuum is described by the new instantons introduced in [5,6,4]. For each spacetime dimension D, we also construct the two different classes of potentials for which the instanton equations are exactly solvable.
We demonstrate that possession of a single negative mode is not a sufficient criterion for an instanton to mediate exponential decay. For example, de Sitter space is generically stable against decay via the Coleman-De Luccia instanton. This is due to the fact that the de Sitter Euclidean action is bounded below, allowing for an approximately de Sitter invariant false vacuum to be constructed.
Bubbles of nothing are a class of vacuum decay processes present in some theories with compactified extra dimensions. We investigate the existence and properties of bubbles of nothing in models where the scalar pseudomoduli controlling the size of the extra dimensions are stabilized at positive vacuum energy, which is a necessary feature of any realistic model. We map the construction of bubbles of nothing to a four-dimensional Coleman-De Luccia problem and establish necessary conditions on the asymptotic behavior of the scalar potential for the existence of suitable solutions. We perform deta…
We study the semiclassical fluctuation problem around bounce solutions for a self-interacting scalar field in curved space. As in flat space, the fluctuation problem separates into partial waves labeled by an integer l, and we determine the large l behavior of the fluctuation determinants, a quantity needed to define a finite fluctuation prefactor. We also show that while the Coleman-De Luccia bounce solution has a single negative mode in the l=0 sector, the oscillating bounce solutions also have negative modes in partial waves higher than the s-wave, further evidence that they are not directl…
Because of the presence of a cosmological horizon the dilute instanton gas approximation used for the derivation of the Coleman-De Luccia tunneling rate in de Sitter spacetime receives additional contributions due to the finite instanton separation. Here I calculate the first corrections to the vacuum decay rate that arise from this effect and depend on the parameters of the theory and the cosmological constant of the background spacetime.
Consistency of the unconventional view of de Sitter space as a quantum theory of gravity with a finite number of degrees of freedom requires that Coleman-De Luccia tunneling rates to vacua with negative cosmological constant should be interpreted as recurrences to low-entropy states. This demand translates into two constraints, or consistency conditions, on the scalar potential which are generically: 1) the distance in field space between the de Sitter vacuum and any other vacuum with negative cosmological constant must be of the order of the reduced Planck mass or larger and 2) the fourth roo…
Thin-wall vacuum decay in the presence of a compact dimension
本文研究了紧致维度存在下假真空衰变问题，推导了驱动真空转变的欧几里得 bounce 配置公式。
Instantons with Quantum Core
本研究提出带量子核的新型瞬子理论，利用量子涨落正则化Coleman理论中的奇异解，建立任意势场下的通用瞬子参数计算方法，弥补了传统薄壁近似的局限，解释了真空不稳定情形下瞬子的存在性。
Singular instantons with finite action
本文研究平坦欧几里得空间中单标量场假真空衰变里的奇异$O(4)$对称瞬子，证明有限作用量要求势能下方无界以规避Coleman定理，并通过两个例子揭示可能存在作用量更低的非$O(4)$对称解。
I provide some simple physical arguments that, once gravitation and some subtleties are taken into account, rather broad classes of potentials result in instantons which tunnel relatively rapidly between perturbatively stable minima. In particular, due to some previously unappreciated technical subtleties, the decay rates for instantons which may be well-described as thin-wall are much larger than the usual Coleman-de Luccia result. I discuss with some level of rigor when the thin-wall approximation holds and clarify some misconceptions regarding the application of this approximation and its m…
In this paper we present supersymmetric instanton and non-supersymmetric wormhole solutions for the universal hypermultiplet sector of $d=4$ N=2 supergravity theories. Instantons and wormholes are constructed as saddle points dominating transition amplitudes between states of definite axionic shift charge, using an approach due to Coleman and Lee. Our solutions are constructed in terms of the conserved Noether charges associated with the global SU(2,1) symmetry of the universal hypermultiplet action. The conditions imposed by regularity on the charges are discussed.
We suggest a technique that explicitly accounts for the structure of an initial state of quantum field in the semiclassical calculations of path integral in curved space-time, and consider decay of metastable state (conformal vacuum of scalar particles above false classical vacuum) in background de Sitter space-time as an example. Making use of this technique, we justify the Coleman-De Luccia approach to the calculation of the decay probability. We propose an interpretation of the Hawking-Moss instanton as a limiting case of constrained instantons. We find that an inverse process of the transi…
D-instantons of Type IIB string theory are Ramond-Ramond counterpart of Giddings-Strominger wormholes connecting two asymptotic regions of spacetime. Such wormholes, according to Coleman, might lead to spacetime topology change, third-quantized baby universes and probabilistic determination of fundamental coupling parameters. Utilizing correspondence between AdS5 x M5 Type IIB supergravity and d=4 super Yang-Mills theory, we point out that topology change and sum over topologies not only take place in string theory but also are required for consistency with holography. Nevertheless, the effect…
We present a calculation of thick-wall Coleman-de-Luccia (CdL) bounces in the Standard Model effective potential in a de Sitter background. The calculation is performed including the effect of the bounce back-reaction on the metric, which we compare with the case of a fixed de-Sitter background, and with similar full-backreaction calculation in a model polynomial potential. The results show that the Standard Model potential exhibits non-trivial behavior: rather than a single CdL solution, there are multiple (non-oscillating) bounce solutions which may contribute to the decay rate. All the extr…
We consider a multi-field open inflation model, in which one of the fields dominates quantum tunneling from a false vacuum while the other field governs slow-roll inflation within the bubble nucleated from false vacuum decay. We call the former the tunneling field and the latter the inflaton field. In the limit of a negligible interaction between the two fields, the false vacuum decay is described by a Coleman-De Luccia instanton. Here we take into account the coupling between the two fields and construct explicitly a multi-field instanton for a simple quartic potential model. We also solve th…
We discuss aspects of the problem of assigning probabilities in eternal inflation. In particular, we investigate a recent suggestion that the lowest energy de Sitter vacuum in the landscape is effectively stable. The associated proposal for probabilities would relegate lower energy vacua to unlikely excursions of a high entropy system. We note that it would also imply that the string theory landscape is experimentally ruled out. However, we extensively analyze the structure of the space of Coleman-De Luccia solutions, and we present analytic arguments, as well as numerical evidence, that the d…
A Unified View of Vacuum Decay Channels
本研究采用隧穿势形式体系，为真空衰变提供统一视角，指出Coleman反弹属于包含Hawking-Moss瞬子、伪反弹等的连续解族。
We consider the fate of AdS vacua connected by tunneling events. A precise holographic dual of thin-walled Coleman--de Luccia bounces is proposed in terms of Fubini instantons in an unstable CFT. This proposal is backed by several qualitative and quantitative checks, including the precise calculation of the instanton action appearing in evaluating the decay rate. Big crunches manifest themselves as time dependent processes which reach the boundary of field space in a finite time. The infinite energy difference involved is identified on the boundary and highlights the ill-defined nature of the …
Brane Nucleation in Supersymmetric Models
本文研究超对称模型中的真空衰变，构建含三形式多重态的超对称拉格朗日量，得到统一两种形式体系的瞬子解，验证超对称极限下的静态解，并探讨其在弦景观宇宙学中的意义。
Evidence for renormalized instantons in real-time simulations of vacuum decay
研究通过相对论标量场零温模拟提取气泡轮廓，对比传统欧几里得瞬子方法与晶格模拟，发现重整化势中的瞬子解能重现测量轮廓并匹配衰变率，证明重整化解释了两种形式主义差异，建立了相关定量联系。
Instantons meet resonances: Unifying two seemingly distinct approaches to quantum tunneling
本文通过展示共振态方法与瞬子方法的等价性，统一了两种看似不同的量子隧穿理论框架。
In this note we perform a synopsis of the life-times from vacuum decay of several de Sitter vacuum constructions in string/M-theory which have a single dS minimum arising from lifting a pre-existing AdS extremum and no other local minima existent after lifting. For these vacua the decay proceeds via a Coleman--De Luccia instanton towards the universal Minkowski minimum at infinite volume. This can be calculated using the thin--wall approximation, provided the cosmological constant of the local dS minimum is tuned sufficiently small. We compare the estimates for the different model classes and …
We study the non-perturbative stability of the Large Volume Scenario (LVS) of IIB string compactifications, by analysing transitions mediated by the Brown-Teitelboim (BT) brane nucleations and by Coleman De Luccia tunneling (CDL). We find that, as long as the effective field theory description holds, the LVS AdS minima are stable despite being non-supersymmetric. This opens the possibility of having a CFT dual. Metastable de Sitter vacua behave differently depending on the uplifting mechanism. We find explicit expressions for the different decay rates in terms of exponentials of the volume. Am…
Using numerical and analytic methods, we study quantum tunneling from a Minkowski false vacuum to an anti-de Sitter true vacuum. Scanning the parameter space of theories with quartic and non-polynomial potentials, we find that for any given potential tunneling is completely quenched if gravitational effects are made sufficiently strong. For potentials where $ε$, the energy density difference between the vacua, is small compared to the barrier height, this occurs in the thin-wall regime studied by Coleman and De Luccia. However, we find that other potentials, possibly with $ε$ much greater than…
Asymptotic limits of constrained instantons
研究标量场假真空衰变中约束瞬子的三种渐近极限：小半径微扰解、大半径薄壁近似（可能不存在）和大拉格朗日乘子极限，通过量纲分析和数值计算得到精确解。
Thin-wall vacuum decay in the presence of a compact dimension meets the $H_0$ and $S_8$ tensions
该研究通过引入5维紧致维度，提出一种机制，利用Casimir力实现AdS到dS的转变，以解决$H_0$和$S_8$张力问题。
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