We reexamine the production of gravitational waves by bubble collisions during a first-order phase transition. The spectrum of the gravitational radiation is determined by numerical simulations using the "envelope approximation". We find that the spectrum rises as f^3.0 for small frequencies and decreases as f^-1.0 for high frequencies. Thus, the fall-off at high frequencies is significantly slower than previously stated in the literature. This result has direct impact on detection prospects for gravity waves originating from a strong first-order electroweak phase transition at space-based interferometers, such as LISA or BBO. In addition, we observe a slight dependence of the peak frequency on the bubble wall velocity.
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…
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 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…
Standard Model Baryon Number Violation at Zero Temperature from Higgs Bubble Collisions
Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器中心）；II. Institute of Theoretical Physics, Universität Hamburg（汉堡大学理论物理第二研究所）；Nordita, KTH Royal Institute of Technology and Stockholm University（诺迪塔，皇家理工学院与斯德哥尔摩大学）；The Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University（斯德哥尔摩大学物理系奥斯克莱因宇宙粒子物理中心）
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 $Ω_{\rm GW} \propto ω^{2.3}$ at low frequencies and $Ω_{\rm GW} \propto ω^{-2.4}$ at high frequencies, marking a significant deviation fr…
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 study the nucleation of a quark gluon plasma (QGP) phase in a hadron gas at low temperatures and high baryon densities. This kind of process will presumably happen very often in nuclear collisions at FAIR and NICA. When the appropriate energy densities (or baryon densities) and temperatures are reached the conversion of one phase into another is not instantaneous. It is a complex process, which involves the nucleation of bubbles of the new phase. One important element of this transition process is the rate of growth of a QGP bubble. In order to estimate it we solve the Relativistic Rayleigh…
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.
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 put forward a novel class of exotic celestial objects that can be produced through phase transitions occurred in the primordial Universe. These objects appear as bubbles of stellar sizes and can be dominated by primordial black holes (PBHs). We report that, due to the processes of Hawking radiation and binary evolution of PBHs inside these stellar bubbles, both electromagnetic and gravitational radiations can be emitted that are featured on the gamma-ray spectra and stochastic gravitational waves (GWs). Our results reveal that, depending on the mass distribution, the exotic stellar bubbles …
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…
Gravitational Wave Signature of Aspherical Bubbles Driven by Thermal Fluctuation
Chongqing University（重庆大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Henan Normal University（河南师范大学）；Shandong University（山东大学）
A model for the acoustic production of gravitational waves at a first order phase transition is presented. The source of gravitational radiation is the sound waves generated by the explosive growth of bubbles of the stable phase. The model assumes that the sound waves are linear and that their power spectrum is determined by the characteristic form of the sound shell around the expanding bubble. The predicted power spectrum has two length scales, the average bubble separation and the sound shell width when the bubbles collide. The peak of the power spectrum is at wavenumbers set by the sound s…
We study a scenario where both dark matter and heavy right handed neutrino (RHN) responsible for leptogenesis acquire masses by crossing the relativistic bubble walls formed as a result of a TeV scale supercooled first order phase transition (FOPT). While this leads to a large out-of-equilibrium abundance of right handed neutrino inside the bubble sufficient to produce the required lepton asymmetry, the dark matter being lighter can still remain in equilibrium with its relic being set by subsequent thermal freeze-out. A classical conformal symmetry ensures the origin of mass via FOPT induced b…
We calculate gravitational wave power spectra from first order early Universe phase transitions using the Sound Shell Model. The model predicts that the power spectrum depends on the mean bubble separation, the phase transition strength, the phase boundary speed, with the overall frequency scale set by the nucleation temperature. There is also a dependence on the time evolution of the bubble nucleation rate. The gravitational wave peak power and frequency are in good agreement with published numerical simulations, where bubbles are nucleated simultaneously. Agreement is particularly good for d…
We study gravitational-wave production from bubble collisions in a cosmic first-order phase transition, focusing on the possibility of model separation by the bubble nucleation rate dependence of the resulting gravitational-wave spectrum. By using the method of relating the spectrum with the two-point correlator of the energy-momentum tensor $\left< T(x)T(y) \right>$, we first write down analytic expressions for the spectrum with a Gaussian correction to the commonly used nucleation rate, $Γ\propto e^{βt}\rightarrow e^{βt-γ^2t^2}$, under the thin-wall and envelope approximations. Then we quant…
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…
