Vacuum Bubbles Research Articles

Schwarzschild-like topological solitons

We construct the first class of topological solitons in gravity that are supported by internal electromagnetic flux with vanishing net charges. The solutions are obtained in a six-dimensional Einstein-Maxwell theory with a three-form flux, and admit an uplift to type IIB supergravity on T4. They are asymptotic to a torus fibration over four-dimensional Minkowski spacetime. An interesting class corresponds to solitons with a BPS particle and its anti-BPS partner held apart by a vacuum bubble. In type IIB, they correspond to bound states of BPS and anti-BPS D1-D5 extremal black holes. These metrics are a particular limit of a larger class of axially symmetric metrics that we construct and that describe smooth horizonless topological solitons. They correspond to bound states of three non-BPS bubbles on a line. An important achievement is that the outer bubbles can carry arbitrary D1-D5 charges that we can tune to vanishing net charges. We discuss their properties and compare them to a four-dimensional Schwarzschild black hole of the same mass. We show that they have a long throat with a large redshift, and that they are ultra-compact with a characteristic size of 1.52 times the Schwarzschild radius.

Annihilogenesis

We investigate a novel interplay between the decay and annihilation of a particle whose mass undergoes a large shift during a first order phase transition, leading to the particles becoming trapped in the false vacuum and enhancing their annihilation rates as the bubbles of true vacuum expand. This opens up a large region of the parameter space where annihilations can be important. We apply this scenario to baryogenesis, where we find that annihilations can be enhanced enough to generate the required baryon asymmetry even for relatively tiny annihilation cross sections with modest CP asymmetries.

Filtered baryogenesis

We propose a new mechanism to simultaneously explain the observed dark matter abundance and the baryon asymmetry of the Universe. The mechanism is based on the Filtered Dark Matter scenario, where dark matter particles acquire a large mass during a first-order phase transition. This implies that only a small fraction of them are energetic enough to enter the advancing true vacuum bubbles and survive until today, while the rest are reflected and annihilate away quickly. We supplement this scenario with a CP-violating interaction, which creates a chiral asymmetry in the population of dark matter particles. In the false vacuum phase, a portal interaction quickly converts the dark sector chiral asymmetry into a Standard Model lepton asymmetry. The lepton asymmetry is then partially converted to a baryon asymmetry by standard electroweak sphaleron processes. We discuss the dependence of the generated asymmetry on the parameters of the model for two different portal interactions and demonstrate successful baryogenesis for both. For one of the portals, it is also possible to simultaneously explain the observed dark matter abundance, over many orders of magnitude in the dark matter mass.

Tadpoles and vacuum bubbles in light-front quantization

We develop a method by which vacuum transitions may be included in light-front calculations. This allows tadpole contributions which are important for symmetry-breaking effects and yet are missing from standard light-front calculations. These transitions also dictate a nontrivial vacuum and contributions from vacuum bubbles to physical states. In nonperturbative calculations these separate classes of contributions (tadpoles and bubbles) cannot be filtered; instead, we regulate the bubbles and subtract the vacuum energy from the eigenenergy of physical states. The key is replacement of momentum-conserving delta functions with model functions of finite width; the width becomes the regulator and is removed after subtractions. The approach is illustrated in free scalar theory, in quenched scalar Yukawa theory, and in a limited Fock-space truncation of ${\ensuremath{\phi}}^{4}$ theory.

How Do We Know if We Live in a Multivariate Universe?

This paper reviews two studies that deal with the simulation of false vacuum bubble collisions and decay, and proposes that searching for evidence of particle scattering outcomes that would result from false vacuum bubble collisions in the CMBR could support the inflationary multiverse hypothesis.

Primordial black holes from spectator field bubbles

We study the evolution of light spectator fields in an asymmetric polynomial potential. During inflation, stochastic fluctuations displace the spectator field from the global minimum of its potential, populating the false vacuum state and thereby allowing for the formation of false vacuum bubbles. By using a lattice simulation, we show that these bubbles begin to contract once they re-enter the horizon and, if sufficiently large, collapse into black holes. This process generally results in the formation of primordial black holes, which, due to the specific shape of their mass function, are constrained to yield at most 1% of the total dark matter abundance. However, the resulting population can source gravitational wave signals observable at the LIGO-Virgo experiments, provide seeds for supermassive black holes or cause a transient matter-dominated phase in the early Universe.

Vacuum bubble collisions: From microphysics to gravitational waves

We comprehensively study the effects of bubble wall thickness and speed on the gravitational wave emission spectrum of collisions of two vacuum bubbles. We numerically simulate a large dynamical range, making use of symmetry to reduce the dimensionality. The high-frequency slope of the gravitational wave spectrum is shown to depend on the thickness of the bubble wall, becoming steeper for thick-wall bubbles, in agreement with recent fully 3+1 dimensional lattice simulations of many-bubble collisions. This dependence is present, even for highly relativistic bubble wall collisions. We use the reduced dimensionality as an opportunity to investigate dynamical phenomena which may underlie the observed differences in the gravitational wave spectra. These phenomena include `trapping', which occurs most for thin-wall bubbles, and oscillations behind the bubble wall, which occur for thick-wall bubbles.

Possible Planck-scale physical production mechanisms and consequences of negative energies—Initial formulation

Negative energies within the scope of quantum field theories are often attributed to processes that include loops and vacuum bubbles. The negative energy solutions are a byproduct of virtual particles that have no impact in normal spacetime. However, this paper postulates that virtual particles can produce physical effects at the Planck-scale.

Escape from supercooling with or without bubbles: gravitational wave signatures

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 study both of these cases in detail in a simple yet representative model. We determine the duration of the thermal inflation, the curvature power spectrum generated for the scales that exit horizon during the thermal inflation, and the stochastic gravitational wave background from the phase transition. We show that these gravitational waves provide an observable signal from the thermal inflation in almost the entire parameter space of interest. Furthermore, the shape of the gravitational wave spectrum can be used to ascertain how the Universe escaped from supercooling.

Bubble wall velocity at strong coupling

Using the holographic correspondence as a tool, we determine the steady-state velocity of expanding vacuum bubbles nucleated within chiral finite temperature first-order phase transitions occurring in strongly coupled large N QCD-like models. We provide general formulae for the friction force exerted by the plasma on the bubbles and for the steady-state velocity. In the top-down holographic description, the phase transitions are related to changes in the embedding of Dqhbox{-} overline{D}q flavor branes probing the black hole background sourced by a stack of N Dp-branes. We first consider the Witten-Sakai-Sugimoto D4hbox{-} D8hbox{-} overline{D}8 setup, compute the friction force and deduce the equilibrium velocity. Then we extend our analysis to more general setups and to different dimensions. Finally, we briefly compare our results, obtained within a fully non-perturbative framework, to other estimates of the bubble velocity in the literature.

Nonadiabatic dynamics across a first-order quantum phase transition: Quantized bubble nucleation

Metastability is a quintessential feature of first-order quantum phase transitions, which is lost either by dynamical instability or by nucleating bubbles of a true vacuum through quantum tunneling. By considering a drive across the first-order quantum phase transition in the quantum Ising chain in the presence of both transverse and longitudinal fields, we reveal multiple regions in the parameter space where the initial metastable state loses its metastability in successive stages. The mechanism responsible is found to be semidegenerate resonant tunnelings to states with specific bubble sizes. We show that such dynamics of quantized bubble nucleations can be understood in terms of Landau-Zener transitions, which provide quantitative predictions of nucleation probabilities for different bubble sizes.

Examining the end of inflation with primordial black hole mass distribution and gravitational waves

We explicitly construct a double-field inflationary model, which satisfies the latest Planck constraints at the cosmic microwave background (CMB) scales and produces the whole dark matter energy density as primordial black holes (PBHs), in the mass range ${10}^{\ensuremath{-}17}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}\ensuremath{\lesssim}{M}_{\mathrm{PBH}}\ensuremath{\lesssim}{10}^{\ensuremath{-}13}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$. The PBHs can be produced after the end of slow-roll inflation from the bubbles of true vacuum that nucleate during the course of inflation. Obtaining PBHs in this mass range enforces the scale of inflation to be extremely low, ${10}^{\ensuremath{-}7}\ensuremath{\lesssim}H\ensuremath{\lesssim}{10}^{\ensuremath{-}3}\text{ }\text{ }\mathrm{GeV}$, which makes the efforts to observe gravitational waves at the CMB scales futile, although it is high enough to allow for a successful big bang nucleosynthesis. We will show that the shape of the mass distribution of the PBHs is dependent on how inflation ends and the Universe settles from the metastable direction to the true one. End of inflation can also be probed by examining the gravitational waves spectrum. In particular, we show that if exit from the rolling metastable direction to the true vacuum of the potential happens through a first-order phase transition after the end of slow-roll inflation, it leaves behind a stochastic gravitational wave background (SGWB), which is potentially observable by the Laser Interferometer Space Antenna. Examining the mass distribution of PBHs and possible SGWB from the end of inflation, we may be able to gain invaluable information about the end of inflation.

Gravitational waves from colliding vacuum bubbles in gauge theories

We study production of gravitational waves (GWs) in strongly supercooled cosmological phase transitions in gauge theories. We extract from two-bubble lattice simulations the scaling of the GW source, and use it in many-bubble simulations in the thin-wall limit to estimate the resulting GW spectrum. We find that in presence of the gauge field the GW source decays with bubble radius as propto R^{-3} after collisions. This leads to a GW spectrum that follows Omega _{mathrm{GW}} propto omega ^{2.3} at low frequencies and Omega _{mathrm{GW}} propto omega ^{-2.9} at high frequencies, marking a significant deviation from the popular envelope approximation.

A possible mass distribution of primordial black holes implied by LIGO-Virgo

The LIGO-Virgo Collaboration has so far detected around 90 black holes, some of which have masses larger than what were expected from the collapse of stars. The mass distribution of LIGO-Virgo black holes appears to have a peak at ∼ 30M ☉ and two tails on the ends. By assuming that they all have a primordial origin, we analyze the GWTC-1 (O1&O2) and GWTC-2 (O3a) datasets by performing maximum likelihood estimation on a broken power law mass function f(m), with the result f ∝ m 1.2 for m < 35 M ☉ and f ∝ m -4 for m > 35 M ☉. This appears to behave better than the popular log-normal mass function. Surprisingly, such a simple and unique distribution can be realized in our previously proposed mechanism of PBH formation, where the black holes are formed by vacuum bubbles that nucleate during inflation via quantum tunneling. Moreover, this mass distribution can also provide an explanation to supermassive black holes formed at high redshifts.

Phases of holographic interfaces

We compute the phase diagram of the simplest holographic bottom-up model of conformal interfaces. The model consists of a thin domain wall between three-dimensional Anti-de Sitter (AdS) vacua, anchored on a boundary circle. We distinguish five phases depending on the existence of a black hole, the intersection of its horizon with the wall, and the fate of inertial observers. We show that, like the Hawking-Page phase transition, the capture of the wall by the horizon is also a first order transition and comment on its field-theory interpretation. The static solutions of the domain-wall equations include gravitational avatars of the Faraday cage, black holes with negative specific heat, and an intriguing phenomenon of suspended vacuum bubbles corresponding to an exotic interface/anti-interface fusion. Part of our analysis overlaps with recent work by Simidzija and Van Raamsdonk but the interpretation is different.

Transitioning from equal-time to light-front quantization in ϕ24 theory

We use the interpolating coordinates studied by Hornbostel to investigate a transition from equal-time quantization to light-front quantization, in the context of two-dimensional $\phi^4$ theory. A consistent treatment is found to require careful consideration of vacuum bubbles, in a nonperturbative extension of the analysis by Collins. Numerical calculations of the spectrum at fixed box size are shown to yield results equivalent to those of equal-time quantization, except when the interpolating coordinates are pressed toward the light-front limit. In that regime, a fixed box size is inconsistent with an accurate representation of vacuum-bubble contributions and causes a spurious divergence in the spectrum. The light-front limit instead requires the continuum momentum-space limit of infinite box size. The calculation of the vacuum energy density is then shown to be independent of the interpolation parameter, which implies that the light-front limit yields the same spectrum as an equal-time calculation. This emphasizes the importance of zero modes and near-zero modes in a light-front analysis of any theory with nontrivial vacuum structure.

Fate of false vacua in holographic first-order phase transitions

Using the holographic correspondence as a tool, we study the dynamics of first-order phase transitions in strongly coupled gauge theories at finite temperature. Considering an evolution from the large to the small temperature phase, we compute the nucleation rate of bubbles of true vacuum in the metastable phase. For this purpose, we find the relevant configurations (bounces) interpolating between the vacua and we compute the related effective actions. We start by revisiting the compact Randall-Sundrum model at high temperature. Using holographic renormalization, we compute the derivative term in the effective bounce action, that was missing in the literature. Then, we address the full problem within the top-down Witten-Sakai-Sugimoto model. It displays both a confinement/deconfinement and a chiral symmetry breaking/restoration phase transition which, depending on the model parameters, can happen at different critical temperatures. For the confinement/deconfinement case we perform the numerical analysis of an effective description of the transition and also provide analytic expressions using thick and thin wall approximations. For the chiral symmetry transition, we implement a variational approach that allows us to address the challenging non-linear problem stemming from the Dirac-Born-Infeld action.

Vacuum loops in light-front field theory

We demonstrate that vacuum diagrams in the genuine light front (LF) field theory are non-zero, in spite of simple kinematical counter-arguments (positivity and conservation of the LF momentum p+, absence of Fourier zero mode). Using the light-front Hamiltonian (time-ordered) perturbation theory, the vacuum amplitudes in self-interacting scalar λϕ3(1+1) and λϕ4(1+1) models are obtained as p=0 limit of the associated self-energy diagrams, where p is the external momentum. They behave as Cλ2μ−2 in D=2, with μ being the scalar-field mass, or diverge in D=4, in agreement with the usual “equal-time” form of field theory, and with the same value of the constant C. The simplest vacuum diagram with two internal lines is analyzed in detail displaying the subtle role of the small k+ region and its connection to the p=0 limit. However, the vacuum bubbles in the genuine light-front field theory are nonvanishing not due to the Fourier mode carrying LF momentum k+=0 (as is the case in the LF evaluation of the covariant Feynman diagrams), in full accord with the observation that the LF perturbation theory formula breaks down in the exact zero-mode case. This is made explicit using the DLCQ method - the discretized (finite-volume) version of the theory, where the light-front zero modes are manifestly absent, but the vacuum amplitudes still converge to their continuum-theory values with the increasing “harmonic resolution” K.

Exploring Primordial Black Holes from the Multiverse with Optical Telescopes.

Primordial black holes (PBHs) are a viable candidate for dark matter if the PBH masses are in the currently unconstrained "sublunar" mass range. We revisit the possibility that PBHs were produced by nucleation of false vacuum bubbles during inflation. We show that this scenario can produce a population of PBHs that simultaneously accounts for all dark matter, explains the candidate event in the Subaru Hyper Suprime-Cam (HSC) data, and contains both heavy black holes as observed by LIGO and very heavy seeds of supermassive black holes. We demonstrate with numerical studies that future observations of HSC, as well as other optical surveys, such as LSST, will be able to provide a definitive test for this generic PBH formation mechanism if it is the dominant source of dark matter.

Instanton solutions in a model of AdS4/CFT3 correspondence

From the wrapping of the (anti)membranes of 11-dimensional supergravity over , on the internal directions along with an ansatz for its 4-form flux, by solving the original equations and identities, we arrive at scalar differential equations in the Euclidean space; note that the associated bulk solutions and setups break all supersymmeties, parity and scale invariance; the resulting (pseudo) scalar potential, which is Higgs-like with two nearly homogeneous vacua, provides the first-order phase transition and tunneling from the false- to true- vacuum. Here, concentrating on the three (pseudo) scalar modes m2=-2, 4, 10 , which are, in turn, realizable in Wick-rotated and skew-whiffed M2-branes backgrounds, we employ approximate methods and, particularly, Adomian decomposition method to solve the nonlinear second-order partial differential equations, valid in the probe approximation, with the Dirichlet boundary condition or the initial data from a basic exact solution, to get solutions in series expansions near the boundary in different orders of perturbation. Next, making use of the AdS4/CFT3 correspondence rules, after swapping the three fundamental representations of for gravitino, we build the dual singlet operators from the (scalar, fermion and gauge) fields in a 3-dimensional Chern-Simons-matter gauge field theory living on the resultant anti-M2-brnaes; after that, by deforming the corresponding boundary actions with the operators, we get invariant solutions with nonzero finite actions, which ,in turn, are small instantons sitting at the origin of a 3-sphere at infinity, causing instability and mediating false vacuum decay. In other words, the boundary potentials unbounded from below are duals for the collapse of the bulk (thin-wall) vacuum bubbles and big crunch singularities.