Fluctuation-Induced Friction in Bubble-Wall Dynamics of Cosmological First-Order Phase Transitions
Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（杭州高等研究院，中国科学院大学）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）
We study bubble-wall dynamics in cosmological first-order phase transitions in a two-scalar-field model, where the wall is formed by $ϕ$ and an additional real scalar $s$ couples through a portal interaction. We evolve the coupled classical field equations on the lattice and demonstrate that for an initial Bose--Einstein distribution of $s$ fluctuations at the nucleation temperature $T_n$, the resulting patchy background intermittently modulates the local driving pressure on the wall. The wall therefore undergoes alternating episodes of acceleration and deceleration and approaches a quasi-stationary propagation regime with a smaller time-averaged speed than in the decoupled limit. We further identify three familiar propagation profiles -- deflagration, detonation, and hybrid -- distinguished by where the dynamical $s$-sector energy density is concentrated relative to the wall. These effects can impact gravitational wave and baryogenesis predictions.
We present an entirely analytic, leading log order determination of the friction an electroweak bubble wall feels during a first order electroweak phase transition. The friction is dominated by W bosons, and gives a wall velocity parametrically ~ alpha_w, and numerically small, ~ .01 -- 0.1 depending on the Higgs mass.
We revisit the computation of bubble wall friction during a cosmological first-order phase transition, using an extended fluid Ansatz to solve the linearized Boltzmann equation. A singularity is found in the fluctuations of background species as the wall approaches the speed of sound. Using hydrodynamics, we argue that a discontinuity across the speed of sound is expected on general grounds, which manifests itself as the singularity in the solution of the linearized system. We discuss this result in comparison with alternative approaches proposed recently, which find a regular behaviour of the…
The bubble wall velocity is essential for the phase transition dynamics in the early universe and its cosmological implications, such as the energy budget of phase transition gravitational wave and electroweak baryogenesis. One key factor to determine the wall velocity is the collision term that quantifies the interactions between the massive particles in the plasma and the bubble wall. We improve the calculations of the collision term beyond the leading-log approximation, and further obtain more precise bubble wall velocity for a representative effective model.
The first order phase transition proceeds via nucleation and growth of true vacuum bubbles. When charged particles collide with the bubble they could radiate electromagnetic wave. We show that, due to an energy loss of the particles by the radiation, the damping pressure acting on the bubble wall depends on the velocity of the wall even in a thermal equilibrium state.
We present results for the bubble wall velocity and bubble wall thickness during a cosmological first-order phase transition in a condensed form. Our results are for minimal extensions of the Standard Model but in principle are applicable to a much broader class of settings. Our first assumption about the model is that only the electroweak Higgs is obtaining a vacuum expectation value during the phase transition. The second is that most of the friction is produced by electroweak gauge bosons and top quarks. Under these assumptions the bubble wall velocity and thickness can be deduced as a func…
We analyse the dynamics of the relativistic bubble expansion during the first order phase transition focusing on the ultra relativistic velocities $γ\gg 1$. We show that fields much heavier than the scale of the phase transition can significantly contribute to the friction and modify the motion of the bubble wall leading to interesting phenomenological consequences. NLO effects on the friction due to the soft vector field emission are reviewed as well.
Using the liquid instanton model continued into Minkowski space and modified for finite temperature, the energy momentum tensor and the surface tension for buble walls during the QCD phase transition are derived. The resulting surface tension is in agreement with lattice calculations. Application to bubble collisions is discussed.
The electroweak baryogenesis depends on the profile of the CP-violating bubble wall created at the first order phase transition. We attempt to determine it by solving the coupled equations of motion for the moduli and phases of the two Higgs doublets at the transition temperature. A variety of CP-violating bubble walls are classified by boundary conditions. We point out that a sufficiently small explicit CP violation gives nonperturbative effects to yield the baryon asymmetry of the universe.
Recently the thermal friction on an expanding bubble from the cosmic first-order phase transition has been calculated to all orders of the interactions between the bubble wall and thermal plasma, leading to a $γ^2$-scaling instead of the previously estimated $γ^1$-scaling for the thermal friction exerted on a fast-moving bubble wall with a Lorentz factor $γ$. We propose for the first time the effective equation of motion (EOM) for an expanding bubble wall in the presence of an arbitrary $γ$-scaling friction to compute the efficiency factor from bubble collisions, which, in the case of $γ^2$-sc…
We present a general numerical approach to solve the equations for bubble wall profiles in models with more than one scalar field and CP violating phases. We discuss the algorithm as well as several problems associated with it and show some profiles for demonstration found with our method.
We compute the wall velocity in the MSSM. We therefore generalize the SM equations of motion for bubble walls moving through a hot plasma at the electroweak phase transition and calculate the friction terms which describe the viscosity of the plasma. We give the general expressions and apply them to a simple model where stops, tops and W bosons contribute to the friction. In a wide range of parameters including those which fulfil the requirements of baryogenesis we find a wall velocity of order v = 0.05-0.1 much below the SM value.
We solve the equations of motion for a CP violating phase between the two Higgs doublets at the bubble wall of the MSSM electroweak phase transition. Contrary to earlier suggestions, we do not find indications of spontaneous ``transitional'' CP violation in the MSSM. On the other hand, in case there is explicit CP violation in the stop and chargino/neutralino sectors, the relative phase between the Higgses does become space dependent, but only mildly even in the maximal case. We also demonstrate that spontaneous CP violation within the bubble wall could occur, e.g., if the Higgs sector of the …
We analyze Higgs condensate bubble expansion during a first-order electroweak phase transition in the early Universe. The interaction of particles with the bubble wall can be accompanied by the emission of multiple soft gauge bosons. When computed at fixed order in perturbation theory, this process exhibits large logarithmic enhancements which must be resummed to all orders when the wall velocity is large. We perform this resummation both analytically and numerically at leading logarithmic accuracy. The numerical simulation is achieved by means of a particle shower in the broken phase of the e…
We present solutions to the equations of motion for bubble wall profiles in the minimal and a non minimal supersymmetric extension of the Standard model. We discuss the method of the numerical approach and present results for the two models (MSSM and NMSSM). Calculations for the NMSSM were done in collaboration with S.J. Huber and M.G. Schmidt.
From friction scaling to an efficient method for estimating bubble wall velocity
Institute of Fundamental Technological Research of the Polish Academy of Sciences（波兰科学院基础技术研究所）；Nicolaus Copernicus Astronomical Center of the Polish Academy of Sciences（波兰科学院尼古拉·哥白尼天文中心）；Faculty of Physics, University of Warsaw（华沙大学物理系）；Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University（名古屋大学小林-益川粒子起源与宇宙研究所）
Impact of Bubble Nucleation History and Friction on Primordial Black Hole Formation
Regional Centre for Accelerator based Particle Physics, Harish-Chandra Research Institute（哈里斯-钱德拉研究所加速器粒子物理区域中心）；Homi Bhabha National Institute（霍米·巴巴国立研究所）
We compute a net electric current during a first order EWPT arising from the asymmetric propagation of fermion chiral modes due to a CP-violating interaction with the Higgs. The interaction is quantified in terms of a CP-violating phase in the bubble wall that separate both false and true vacuum phases. We comment on the possibility of this current to generate a seed magnetic field and its implications for primordial magne- togenesis in the early Universe.
We study the CP-violating bubble wall by solving the coupled equations of motion derived from the two-Higgs-doublet model for the moduli $ρ_i$ and phases $θ_ i$ of the two scalars $(i=1,2)$ at the transition temperature. We find a solution that the CP-violating phase $θ\equivθ_1-θ_2$ connecting the CP-conserving vacua strongly violates CP in the intermediate region while the moduli largely deviate from the kink shape there. We estimate the chiral charge flux through the wall surface, which may be efficient enough to produce the baryon asymmetry by the sphaleron process.
We consider the question of whether cosmic ray catalysed false vacuum decay can be phenomenologically more important than spontaneous decay via quantum tunnelling. We extend the zero bubble wall width Landau-WKB analysis of catalysed false vacuum decay to include the leading order effects of finite wall width and derive an expression for the thin-wall bubble action. Using this we calculate the exponential suppression factor for the catalysed decay rate at the critical bubble energy, corresponding to the largest probability of catalysed decay. We show that, in general, cosmic ray catalysed deca…
It has been recently shown that meta-stable domain walls exist in high-density QCD ($μ\neq 0$) as well as in QCD with large number of colors ($N_c\to\infty$), with the lifetime being exponentially long in both cases. Such metastable domain walls may exist in our world as well, especially in hot hadronic matter with temperature close to critical. In this paper we discuss what happens if a bubble made of such wall is created in heavy ion collisions, in the mixed phase between QGP and hadronic matter. We show it will further be expanded to larger volume $\sim 20 fm^3$ by the pion pressure, before…
We compute the net electric current generated during a first order electroweak phase transition when fermions transit from the false to the true vacuum. This current is generated by the CP-violating fermion interaction with the Higgs during the phase transition and is quantified in terms of a CP-violating phase in the bubble wall separating the symmetric from the symmetry-broken phases. We comment on the seed magnetic field that this current is able to generate and it is possible implications for magnetogenesis in the early universe during the electroweak phase transition.
We build on existing calculations of the wall velocity of the expanding bubbles of the broken symmetry phase in a first-order electroweak phase transition within the light stop scenario (LSS) of the MSSM. We carry out the analysis using the 2-loop thermal potential for values of the Higgs mass consistent with present experimental bounds. Our approach relies on describing the interaction between the bubble and the hot plasma by a single friction parameter, which we fix by matching to an existing 1-loop computation and extrapolate it to our regime of interest. For a sufficiently strong phase tra…
In extensions of the Standard Model with extra scalars, the electroweak phase transition can be very strong, and the bubble walls can be highly relativistic. We revisit our previous argument that electroweak bubble walls can "run away," that is, achieve extreme ultrarelativistic velocities $γ\sim 10^{14}$. We show that, when particles cross the bubble wall, they can emit transition radiation. Wall-frame soft processes, though suppressed by a power of the coupling $α$, have a significance enhanced by the $γ$-factor of the wall, limiting wall velocities to $γ\sim 1/α$. Though the bubble walls ca…
In cosmological first-order phase transitions, the progress of true-vacuum bubbles is expected to be significantly retarded by the interaction between the bubble wall and the hot plasma. It has been claimed that this leads to a significant reduction in the number of topological defects formed per bubble, as a result of phase equilibration between bubbles. This claim has been verified for spontaneously-broken global symmetries. We perform a series of simulations of complete phase transitions in the 2+1-dimensional U(1)-Abelian Higgs model, for a range of bubble wall velocities, in order to obta…
We discuss the generation of the baryon asymmetry by a strong first order electroweak phase transition in the early universe, particularly in the context of the MSSM. This requires a thorough numerical treatment of the bubble wall profile in the case of two Higgs fields. CP violating complex particle masses varying with the Higgs field in the wall are essential. Since in the MSSM there is no indication of spontaneous CP violation around the critical temperature (contrary to the NMSSM) we have to rely on standard explicit CP violation. Using the WKB approximation for particles in the plasma we …
Standard electroweak baryogenesis in the context of a first order phase transition is effective in generating the baryon asymmetry of the universe if the broken phase bubbles expand at subsonic speed, so that CP asymmetric currents can diffuse in front of the wall. Here we present a new mechanism for electroweak baryogenesis which operates for supersonic bubble walls. It relies on the formation of small bubbles of the symmetric phase behind the bubble wall, in the broken phase, due to the heating of the plasma as the wall passes by. We apply the mechanism to a model in which the Higgs field is…
The dynamics of false vacuum decay at the end of inflation is studied. It is shown that the creation of a new phase is mainly stimulated by temperature fluctuations. Moving walls of O(3)-symmetric bubbles weakly interact with their surroundings at the inflation stage. Large field fluctuations might arise as a result of wall collisions.
In extensions of the Standard Model with SU(2) singlet scalar fields, there can be regions of parameter space for which the electroweak phase transition is first order already at the mean-field level of analysis. We show that in this case the phase interface (bubble wall) can become ultra-relativistic, with the relativistic gamma factor gamma = (1-v_{wall}^2)^{-1/2} growing linearly with the wall's propagation distance. We provide a simple criterion for determining whether the bubble wall "runs away" in this way or if gamma approaches a terminal value.
During a cosmological first-order phase transition, particles of the plasma crossing the bubble walls can radiate a gauge boson. The resulting pressure cannot be computed perturbatively for large coupling constant and/or large supercooling. We resum the real and virtual emissions at all leading-log orders, both analytically and numerically using a Monte-Carlo simulation. We find that radiated bosons are dominantly soft and that the resulting retarding pressure on relativistic bubble walls is linear both in the Lorentz boost and in the order parameter, up to a log. We further quantitatively dis…
We study statistical relationships between bubble walls in cosmological first-order phase transitions. We consider the conditional and joint probabilities for different points on the walls to remain uncollided at given times. We use these results to discuss space and time correlations of bubble walls and their relevance for the consequences of the transition. In our statistical treatment, the kinematics of bubble nucleation and growth is characterized by the nucleation rate and the wall velocity as functions of time. We obtain general expressions in terms of these two quantities, and we consid…
In first-order cosmological phase transitions, the asymptotic velocity of expanding bubbles is of crucial relevance for predicting observables like the spectrum of stochastic gravitational waves, or for establishing the viability of mechanisms explaining fundamental properties of the universe such as the observed baryon asymmetry. In these dynamic phase transitions, it is generally accepted that subluminal bubble expansion requires out-of-equilibrium interactions with the plasma which are captured by friction terms in the equations of motion for the scalar field. This has been disputed in work…
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 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 re…
In cosmological first-order phase transitions, gravitational waves are generated by the collisions of bubble walls and by the bulk motions caused in the fluid. A sizeable signal may result from fast-moving walls. In this work we study the hydrodynamics associated to the fastest propagation modes, namely, ultra-relativistic detonations and runaway solutions. We compute the energy injected by the phase transition into the fluid and the energy which accumulates in the bubble walls. We provide analytic approximations and fits as functions of the net force acting on the wall, which can be readily e…
We present a general method for computing the gravitational radiation arising from the motion of bubble walls or thin fluid shells in cosmological phase transitions. We discuss the application of this method to different wall kinematics. In particular, we derive general expressions for the bubble collision mechanism in the envelope approximation and the so-called bulk flow model, and we also consider deformations from the spherical bubble shape. We calculate the gravitational wave spectrum for a specific model of deformations on a definite size scale, which gives a peak away from that of the b…
The cosmological remnants of a first-order phase transition generally depend on the perturbations that the walls of expanding bubbles originate in the plasma. Several of the formation mechanisms occur when bubbles collide and lose their spherical symmetry. However, spherical bubbles are often considered in the literature, in particular for the calculation of gravitational waves. We study the steady state motion of bubble walls for different bubble symmetries. Using the bag equation of state, we discuss the propagation of phase transition fronts as detonations and subsonic or supersonic deflagr…
Thermal Masses and Bubble-Wall Friction in Cosmological Phase Transitions
Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；INFN Sezione di Firenze（佛罗伦萨大学INFN分部）；Dipartimento di Fisica, Università della Calabria（卡拉布里亚大学物理系）；INFN, Gruppo Collegato di Cosenza（科森扎联合INFN小组）；Dipartimento di Fisica, Sapienza University of Rome and INFN（罗马智慧大学物理系及INFN）；Dipartimento di Fisica e Astronomia, Università di Firenze（佛罗伦萨大学物理与天文学系）；Department of Physics and Astronomy, University of Sussex（苏塞克斯大学物理与天文学系）
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…
