We study the magnetic fields generation from the cosmological first-order electroweak phase transition. We calculate the magnetic field induced by the variation of the Higgs phase for two bubbles and three bubbles collisions. Our study shows that electromagnetic currents in the collision direction produce the ring-like magnetic field in the intersect regions of colliding bubbles, which may seed the primordial magnetic field that are constrained by intergalatic field observations.
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 …
We study scalar bubble collisions in first-order phase transitions focusing on the relativistic limit. We propose 'trapping equation' which describes the wall behavior after collision, and test it with numerical simulations in several setups. We also examine the energy dynamics after collision and discuss its implications to gravitational wave production.
We study strongly supercooled cosmological phase transitions. We perform numerical lattice simulations of two-bubble collisions and demonstrate that, depending on the scalar potential, in the collision the field can either bounce to a false vacuum or remain oscillating around the true vacuum. We study if these cases can be distinguished from their gravitational wave signals and discuss the possibility of black hole formation in the bubble collisions.
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…
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 study the gravitational radiation produced by the collisions of bubble walls or thin fluid shells in cosmological phase transitions. Using the so-called envelope approximation, we obtain analytically the asymptotic behavior of the gravitational wave spectrum at low and high frequencies for any phase transition model. The complete spectrum can thus be approximated by a simple interpolation between these asymptotes. We verify this approximation with specific examples. We use these results to discuss the dependence of the spectrum on the time and size scales of the source.
We explore the collision of two cylindrical bubbles in classical general relativity with a scalar field stress-energy tensor. Inside each bubble the field rests at a local minimum of the potential with non-negative energy density. Outside the field rests at zero potential, the global minimum. The calculation resolves the connection from the inner de-Sitter region to the asymptotically flat Minkowski spacetime. We choose initial conditions such that the two bubbles collide and study the full nonlinear evolution by means of a two-dimensional numerical simulation of Einstein's equations. The coll…
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 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…
Abdus Salam Centre for Theoretical Physics, Imperial College London（阿卜杜斯·萨拉姆理论物理中心，伦敦帝国理工学院）；Theoretical Physics Department, CERN（欧洲核子研究组织理论物理部）；Rudolf Peierls Centre for Theoretical Physics, University of Oxford（牛津大学鲁道夫·皮尔斯理论物理中心）；Laboratoire de Physique de l’École Normale Supérieure, Université PSL（巴黎高等师范学院物理实验室，PSL大学）
We estimate the gravitational wave spectra generated in strongly supercooled phase transitions by bubble collisions and fluid motion. We derive analytically in the thin-wall approximation the efficiency factor that determines the share of the energy released in the transition between the scalar field and the fluid. We perform numerical simulations including the efficiency factor as a function of bubble radius separately for all points on the bubble surfaces to take into account their different collision times. We find that the efficiency factor does not significantly change the gravitational w…
We consider gravitational wave production by bubble collisions during a cosmological first-order phase transition. In the literature, such spectra have been estimated by simulating the bubble dynamics, under so-called thin-wall and envelope approximations in a flat background metric. However, we show that, within these assumptions, the gravitational wave spectrum can be estimated in an analytic way. Our estimation is based on the observation that the two-point correlator of the energy-momentum tensor $\langle T(x)T(y)\rangle$ can be expressed analytically under these assumptions. Though the fi…
宇宙气泡是通过量子隧穿过程成核的。成核后，它们会膨胀并相互碰撞。在本文中，我们特别关注的两个相同大小的气泡碰撞和计算的引力波发射的碰撞。首先，我们利用实标量场及其四次势研究了碰撞机制。然后，使用这个模型，我们计算引力波的碰撞在一个简单的方式。在四极近似下，能量-动量张量直接用标量场、局部几何和势表示，通过对波源体积积分得到时域引力波形。我们提出的引力波形发射过程中（i）的初始到中间阶段的强碰撞和（ii）弱碰撞的最后阶段：前者得到的数值，在\textit{full General Relativity}和后者解析，在平坦的时空近似。我们从气泡碰撞中获得了对时域引力波形的定性认识：在（i）期间，波形显示出碰撞的非线性，其特征在于调制频率和尖点状凸起，而在（ii）期间，波形显示出碰撞的线性，其特征在于平滑的单色振荡。
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…
We propose a novel mechanism for production of baryonic asymmetry in the early Universe. The mechanism takes advantage of the strong first order phase transition that produces runaway bubbles in the hidden sector that propagate almost without friction with ultra-relativistic velocities. Collisions of such bubbles can non-thermally produce heavy particles that further decay out-of-equilibrium into the SM and produce the observed baryonic asymmetry. This process can proceed at the very low temperatures, providing a new mechanism of post-sphaleron baryogenesis. In this paper we present a fully ca…
Making use of both the stochastic approach to the tunneling phenomenon and the threshold statistics, we offer a simple argument to show that critical bubbles may be correlated in first-order phase transitions and biased compared to the underlying scalar field spatial distribution. This happens though only if the typical energy scale of the phase transition is sufficiently high. We briefly discuss possible implications of this result, e.g. the formation of primordial black holes through bubble collisions.
We study the envelope approximation and its applicability to first-order phase transitions in the early universe. We demonstrate that the power laws seen in previous studies exist independently of the nucleation rate. We also compare the envelope approximation prediction to results from large-scale phase transition simulations. For phase transitions where the contribution to gravitational waves from scalar fields dominates over that from the coupled plasma of light particles, the envelope approximation is in agreement, giving a power spectrum of the same form and order of magnitude. In all oth…
Eternal inflation bubble collision signature on CMB remote dipole and quadrupole fields
Shanghai Jiao Tong University（上海交通大学）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交大李政道研究所）；Dunlap Institute for Astronomy and Astrophysics, University of Toronto（多伦多大学邓普天文学与天体物理研究所）
We derive efficiency factors for the production of gravitational waves through bubble collisions and plasma-related sources in strong phase transitions, and find the conditions under which the bubble collisions can contribute significantly to the signal. We use lattice simulations to clarify the dependence of the colliding bubbles on their initial state. We illustrate our findings in two examples, the Standard Model with an extra $|H|^6$ interaction and a classically scale-invariant $U(1)_{\rm B-L}$ extension of the Standard Model. The contribution to the GW spectrum from bubble collisions is …
The dispersion measure (DM) of high-redshift $(z \gtrsim 6)$ transient objects such as Fast Radio Bursts can be a powerful tool to probe the intergalactic medium during the Epoch of Reionization. In this paper, we study the variance of the DMs of objects with the same redshift as a potential probe of the size distribution of ionized bubbles. We calculate the DM variance with a simple model with randomly-distributed spherical bubbles. It is found that the DM variance reflects the characteristics of the probability distribution of the bubble size. We find the variance can be measured precisely e…
Double-layered vacuum bubbles and cosmological phase transitions
School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（杭州高等研究院基础物理与数学学院，中国科学院大学）；School of Physical Sciences, University of Chinese Academy of Sciences（物理科学学院，中国科学院大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（理论物理研究所，中国科学院）；School of Physics and Astronomy, Sun Yat-sen University（物理与天文学院，中山大学）
A possible way to study the reionization of cosmic hydrogen is by observing the large ionized regions (bubbles) around bright individual sources, e.g., quasars, using the redshifted 21 cm signal. It has already been shown that matched filter-based methods are not only able to detect the weak 21 cm signal from these bubbles but also aid in constraining their properties. In this work, we extend the previous studies to develop a rigorous Bayesian framework to explore the possibility of constraining the parameters that characterize the bubbles. To check the accuracy with which we can recover the b…
