Motivated by the difficulty of constructing de Sitter vacua in string theory, a new approach was proposed in arXiv:1807.01570 and arXiv:1907.04268, where four dimensional de Sitter space was realized as the effective cosmology, with matter and radiation, on an expanding spherical bubble that mediates the decay of non supersymmetric $AdS_5$ to a more stable $AdS_5$ in string theory. In this third installment, we further expand on this scenario by considering the backreaction of matter in the bulk and on the brane in terms of how the brane bends. We compute the back reacted metric on the bent brane as well as in the five dimensional bulk. To further illuminate the effect of brane-bending, we compare our results with an explicit computation of the five dimensional graviton propagator using a holographic prescription. Finally we comment on a possible localization of four dimensional gravity in our model using two colliding branes.
Cosmological phase transitions proceed via the nucleation of bubbles that subsequently expand and collide. The resulting gravitational wave spectrum depends crucially on the bubble wall velocity. Microscopic calculations of this velocity are challenging even in weakly coupled theories. We use holography to compute the wall velocity from first principles in a strongly coupled, non-Abelian, four-dimensional gauge theory. The wall velocity is determined dynamically in terms of the nucleation temperature. We find an approximately linear relation between the velocity and the ratio $Δ\mathcal{P}/\ma…
We perform large-scale real-time simulations of a bubble wall sweeping through an out-of-equilibrium plasma. The scenario we have in mind is the electroweak phase transition, which may be first order in extensions of the Standard Model, and produce such bubbles. The process may be responsible for baryogenesis and can generate a background of primordial cosmological gravitational waves. We study thermodynamic features of the plasma near the advancing wall, the generation of Chern-Simons number/Higgs winding number and consider the potential for CP-violation at the wall generating a baryon asymm…
We discuss the dynamics of expanding bubble walls in the presence of massive dark photons whose mass changes as they cross the wall. For sufficiently thin walls, we show that there exists a transient kinematic regime characterized by a constant reflection probability of longitudinal -- but not transverse -- modes. This effect can have important implications for the dynamics of expanding vacuum bubbles in the early Universe. Most notably, it leads to a new source of pressure on the expanding interface, featuring a non-monotonic dependence on the $γ$-factor of the bubble walls and reaching a pea…
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.
A model that gives rise to vacuum bubbles is considered where the domain wall field interacts with another real scalar field, resulting in the formation of domain ribbons within the host domain wall. Ribbon-antiribbon annihilations produce elementary bosons whose mass inside the wall is different from the mass in vacuum. Two cases are considered, where the bosons get trapped either within the bubble wall or the bosons get trapped within the vacuum enclosed by the bubble. The bosonic (meta)stabilization effect on the bubble is examined in each case. It is found that when the bosons become trapp…
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 study the dynamics of bubble wall in five-dimensional Gauss-Bonnet gravity in the thin-wall approximation. The motion of the domain wall is determined by the generalized Israel junction condition. We find a solution where the wall of true vacuum bubble is oscillating, the breathing bubbles. We briefly comment on how this breathing vacuum bubble can affect the analysis of the string theory landscape.
Kobe University（神户大学）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交大凌波书院）；School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）
We present semi-analytic techniques for finding bubble wall profiles during first order phase transitions with multiple scalar fields. Our method involves reducing the problem to an equation with a single field, finding an analytic solution and perturbing around it. The perturbations can be written in a semi-analytic form. We argue that our technique lacks convergence problems and demonstrate the speed of convergence on an example potential.
Negative mass makes perfect physical sense as long as the dominant energy condition is satisfied by the corresponding energy-momentum tensor. Heretofore, only {\it configurations} of negative mass had been found \cite{Belletete:2013nqa,Mbarek:2014ppa}, the analysis did not address stability or dynamics. In this paper, we analyze both of these criteria. We demonstrate the existence of {\it stable}, static, negative mass bubbles in an asymptotically de Sitter space-time. The bubbles are solutions of the Einstein equations and correspond to an interior region of space-time containing a specific m…
It is commonly expected that a friction force on the bubble wall in a first-order phase transition can only arise from a departure from thermal equilibrium in the plasma. Recently however, it was argued that an effective friction, scaling as $γ_w^2$ (with $γ_w$ being the Lorentz factor for the bubble wall velocity), persists in local equilibrium. This was derived assuming constant plasma temperature and velocity throughout the wall. On the other hand, it is known that, at the leading order in derivatives, the plasma in local equilibrium only contributes a correction to the zero-temperature pot…
We derive a general quantum field theoretic formula for the force acting on expanding bubbles of a first order phase transition in the early Universe setting. In the thermodynamic limit the force is proportional to the entropy increase across the bubble of active species that exert a force on the bubble interface. When local thermal equilibrium is attained, we find a strong friction force which grows as the Lorentz factor squared, such that the bubbles quickly reach stationary state and cannot run away. We also study an opposite case when scatterings are negligible across the wall (ballistic l…
We study gravitational-wave production from bubble dynamics (bubble collisions and sound waves) during a cosmic first-order phase transition with an analytic approach. We first propose modeling the system with the thin-wall approximation but without the envelope approximation often adopted in the literature, in order to take bubble propagation after collisions into account. The bubble walls in our setup are considered as modeling the scalar field configuration and/or the bulk motion of the fluid. We next write down analytic expressions for the gravitational-wave spectrum, and evaluate them wit…
We discuss a holographic description of vacuum bubbles, with possible implications for a consistent description of the multiverse. In particular, we elaborate on the recent observation by Maldacena, that the interior of AdS bubbles can be described in terms of CFT degrees of freedom living on the worldsheet of the bubble wall. We consider the scattering of bulk gravitons in the ambient parent vacuum, off the bubble wall. In the dual description, the transmission coefficient is interpreted as the probability that a graviton is absorbed by the worldsheet CFT degrees of freedom. The result is in …
Inhomogeneous solutions of the gap equation in the mean field approach to Nambu-Jona-Lasinio model are studied. An approximate Ginzburg-Landau-like gap equation is obtained and the domain wall solution is found. Binding of fermions to the domain wall is demonstrated. Compact domain wall with bound fermions is studied and stabilisation by fermion pressure is demonstrated which opens a possibility for existence of "soap bubble" hadronic states.
We obtain full moduli parameters for generic non-planar BPS networks of domain walls in an extended Abelian-Higgs model with $N$ complex scalar fields, and exhaust all exact solutions in the corresponding $\mathbb{C}P^{N -1}$ model. We develop a convenient description by grid diagrams which are polytopes determined by mass parameters of the model. To illustrate the validity of our method, we work out non-planar domain wall networks for lower $N$ in $3+1$ dimensions. In general, the networks can have compact vacuum bubbles, which are finite vacuum regions surrounded by domain walls, when the po…
First order phase transitions could play a major role in the early universe, providing important phenomenological consequences, such as the production of gravitational waves and the generation of baryon asymmetry. An important aspect that determines the properties of the phase transition is the dynamics of the true-vacuum bubbles, which is controlled by the density perturbations in the hot plasma. We study this aspect presenting, for the first time, the full solution of the linearized Boltzmann equation for the top quark species coupled to the Higgs field during a first-order electroweak phase…
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 $Dq$-${\bar Dq}$ flavor branes probing the black hole background sourced by a stack of $N$ $Dp$-branes. We first consider the …
It has recently been shown in high resolution numerical simulations that relativistic collisions of bubbles in the context of a multi-vacua potential may lead to the creation of bubbles in a new vacuum. In this paper, we show that scalar fields with only potential interactions behave like free fields during high-speed collisions; the kick received by them in a collision can be deduced simply by a linear superposition of the bubble wall profiles. This process is equivalent to the scattering of solitons in 1+1 dimensions. We deduce an expression for the field excursion (shortly after a collision…
We study domain-walls and bubble nucleation in a non-relativistic vector field theory with different longitudinal and transverse speeds of sound. We describe analytical and numerical methods to calculate the orientation dependent domain-wall tension, $σ(θ)$. We then use this tension to calculate the critical bubble shape. The longitudinally oriented domain-wall tends to be the heaviest, and sometime suffers an instability. It can spontaneously break into zigzag segments. In this case, the critical bubble develops kinks, and its energy, and therefore the tunneling rate, scales with the sound sp…
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…
We study the possible types of the nucleation of vacuum bubbles. We classify vacuum bubbles in de Sitter background and present some numerical solutions. The thin-wall approximation is employed to obtain the nucleation rate and the radius of vacuum bubbles. With careful analysis we confirm that Parke's formula is also applicable to the large true vacuum bubbles. The nucleation of the false vacuum bubble in de Sitter background is also evaluated. The tunneling process in the potential with degenerate vacua is analyzed as the limiting cases of the large true vacuum bubble and false vacuum bubble…
We develop a set of controlled, analytic approximations to study the effects of bubble collisions on cosmology. We expand the initial perturbation to the inflaton field caused by the collision in a general power series, and determine its time evolution during inflation in terms of the coefficients in the expansion. In models where the observer's bubble undergoes sufficient slow-roll inflation to solve the flatness problem, in the thin wall limit only one coefficient in the expansion is relevant to observational cosmology, allowing nearly model-independent predictions. We discuss two approaches…
We study collisions between nearly planar domain walls including the effects of small initial nonplanar fluctuations. These perturbations represent the small fluctuations that must exist in a quantum treatment of the problem. In a previous paper, we demonstrated that at the linear level a subset of these fluctuations experience parametric amplification as a result of their coupling to the planar symmetric background. Here we study the full three-dimensional nonlinear dynamics using lattice simulations, including both the early time regime when the fluctuations are well described by linear pert…
