Cosmological First-order Phase Transition Research Articles

Estimating the uncertainty of cosmological first order phase transitions with numerical simulations of bubble nucleation

In order to study the validity of analytical formulas used in the calculation of characteristic physical quantities related to vacuum bubbles, we conduct several numerical simulations of bubble kinematics in the context of cosmological first-order phase transitions to determine potentially existing systematic uncertainties. By comparing with the analytical results, we obtain the following observations: (1) The simulated false vacuum fraction will approach the theoretical one with increasing simulated volume. When the side length of the cubic simulation volume becomes larger than 14.5βth−1, the simulated results do not change significantly. (2) The theoretical expected total number of bubbles do not agree with the simulated ones, which may be caused by the inconsistent use of the false vacuum fraction formula. (3) The different nucleation rate prefactors do not affect the bubble kinetics much. (4) The lifetime distribution in the sound shell model does not obey an exponential distribution, in such a way as to cause a suppression in the gravitational wave spectra. Published by the American Physical Society 2024

Primordial black holes from supercooled phase transitions

Cosmological first-order phase transitions (1stOPTs) are said to be strongly supercooled when the nucleation temperature is much smaller than the critical temperature. These are often encountered in theories that admit a nearly scale-invariant potential, for which the bounce action decreases only logarithmically with temperature. During supercooled 1stOPTs the equation of state of the universe undergoes a rapid and drastic change, transitioning from vacuum domination to radiation domination. The statistical variations in bubble nucleation histories imply that distinct causal patches percolate at slightly different times. Patches which percolate the latest undergo the longest vacuum-domination stage and as a consequence develop large overdensities triggering their collapse into primordial black holes (PBHs). We derive an analytical approximation for the probability of a patch to collapse into a PBH as a function of the 1stOPT duration, β−1, and deduce the expected PBH abundance. We find that 1stOPTs which take more than 15% of a Hubble time to complete (β/H≲7) produce observable PBHs. Their abundance is independent of the duration of the supercooling phase, in agreement with the de Sitter no hair conjecture. Published by the American Physical Society 2024

General backreaction force of cosmological bubble expansion

The gravitational-wave energy-density spectra from cosmological first-order phase transitions crucially depend on the terminal wall velocity of asymptotic bubble expansion when the driving force from the effective potential difference is gradually balanced by the backreaction force from the thermal plasma. Much attention has previously focused on the backreaction force acting on the bubble wall alone but overlooked the backreaction forces on the sound shell and shock-wave front, if any, which have been both numerically and analytically accomplished in our previous studies but only for a bag equation of state. In this paper, we will generalize the backreaction force on bubble expansion beyond the simple bag model. Published by the American Physical Society 2024

Gauged Q-ball dark matter through a cosmological first-order phase transition

As a new type of dynamical dark matter mechanism, we discuss the stability of the gauged Q-ball dark matter and its production mechanism through a cosmological first-order phase transition. This work delves into the study of gauged Q-ball dark matter generated during the cosmic phase transition. We demonstrate detailed discussions on the stability of gauged Q-balls to rigorously constrain their charge and mass ranges. Additionally, employing analytic approximations and the mapping method, we provide qualitative insights into gauged Q-balls. We establish an upper limit on the gauge coupling constant and give the relic density of stable gauged Q-ball dark matter formed during a first-order phase transition. Furthermore, we discuss potential observational signatures or constraints of gauged Q-ball dark matter, including astronomical observations and gravitational wave signals.

A-B Transition in Superfluid 3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^3$$\\end{document}He and Cosmological Phase Transitions

First-order phase transitions in the very early universe are a prediction of many extensions of the Standard Model of particle physics and could provide the departure from equilibrium needed for a dynamical explanation of the baryon asymmetry of the Universe. They could also produce gravitational waves of a frequency observable by future space-based detectors such as the Laser Interferometer Space Antenna. All calculations of the gravitational wave power spectrum rely on a relativistic version of the classical nucleation theory of Cahn-Hilliard and Langer, due to Coleman and Linde. The high purity and precise control of pressure and temperature achievable in the laboratory made the first-order A to B transition of superfluid 3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^3$$\\end{document}He ideal for test of classical nucleation theory. As Leggett and others have noted, the theory fails dramatically. The lifetime of the metastable A phase is measurable, typically of order minutes to hours, far faster than classical nucleation theory predicts. If the nucleation of B phase from the supercooled A phase is due to a new, rapid intrinsic mechanism that would have implications for first-order cosmological phase transitions as well as predictions for gravitational wave production in the early universe. Here we discuss studies of the A-B phase transition dynamics in 3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^3$$\\end{document}He, both experimental and theoretical, and show how the computational technology for cosmological phase transition can be used to simulate the dynamics of the A-B transition, support the experimental investigations of the A-B transition in the QUEST-DMC collaboration with the goal of identifying and quantifying the mechanism(s) responsible for nucleation of stable phases in ultra-pure metastable quantum phases.

Cosmological first-order vacuum phase transitions in an expanding anisotropic universe

We examine the anisotropy originated from a first-order vacuum phase transitions through three-dimensional numerical simulations. We apply Bianchi Type-I metric to our model that has one scalar field minimally coupled to the gravity. We calculate the time evolution of the energy density for the shear scalar and the directional Hubble parameters as well as the power spectra for the scalar field and the gravitational radiation although there are a number of caveats for the tensor perturbations in Bianchi Type-I universe. We run simulations with different mass scales of the scalar field, therefore, in addition to investigation of anisotropy via the shear scalar, we also determine at which mass scale the phase transition completes successfully, hence, neglecting the expansion of the Universe does not significantly affect the results. Finally, we showed that such an event may contribute to the total anisotropy depending on the mass scale of the scalar field and the initial population of nucleated bubbles.

General bubble expansion at strong coupling

The strongly coupled system like the quark-hadron transition (if it is of first order) is becoming an active play yard for the physics of cosmological first-order phase transitions. However, the traditional field theoretic approach to strongly coupled first-order phase transitions is of great challenge, driving recent efforts from holographic dual theories with explicit numerical simulations. These holographic numerical simulations have revealed an intriguing linear correlation between the phase pressure difference (pressure difference away from the wall) to the nonrelativistic terminal velocity of an expanding planar wall, which has been reproduced analytically alongside both cylindrical and spherical walls from perfect-fluid hydrodynamics in our previous study but only for a bag equation of state. We also found, in our previous study, a universal quadratic correlation between the wall pressure difference (pressure difference near the bubble wall) to the nonrelativistic terminal wall velocity regardless of wall geometries. In this paper, we will generalize these analytic relations between the phase/wall pressure difference and terminal wall velocity into a more realistic equation of state beyond the simple bag model, providing the most general predictions so far for future tests from holographic numerical simulations of strongly coupled first-order phase transitions. Published by the American Physical Society 2024

Bubble-wall velocity in local thermal equilibrium: hydrodynamical simulations vs analytical treatment

We perform real-time hydrodynamical simulations of the growth of bubbles formed during cosmological first-order phase transitions under the assumption of local thermal equilibrium. We confirm that pure hydrodynamic backreaction can lead to steady-state expansion and that bubble-wall velocity in such case agrees very well with the analytical estimates. However, this is not the generic outcome. Instead, it is much more common to observe runaways, as the early-stage dynamics right after the nucleation allow the bubble walls to achieve supersonic velocities before the heated fluid shell in front of the bubble is formed. This effect is not captured by other methods of calculation of the bubble-wall velocity which assume stationary solutions to exist at all times and would have a crucial impact on the possible generation of both baryon asymmetry and gravitational wave signals.

Does NANOGrav observe a dark sector phase transition?

Gravitational waves from a first-order cosmological phase transition, at temperatures at the MeV-scale, would arguably be the most exciting explanation of the common red spectrum reported by the NANOGrav collaboration, not the least because this would be direct evidence of physics beyond the standard model. Here we perform a detailed analysis of whether such an interpretation is consistent with constraints on the released energy deriving from big bang nucleosynthesis and the cosmic microwave background. We find that a phase transition in a completely secluded dark sector with sub-horizon sized bubbles is strongly disfavoured with respect to the more conventional astrophysical explanation of the putative gravitational wave signal in terms of supermassive black hole binaries. On the other hand, a phase transition in a dark sector that subsequently decays, before the time of neutrino decoupling, remains an intriguing possibility to explain the data. From the model-building perspective, such an option is easily satisfied for couplings with the visible sector that are small enough to evade current collider and astrophysical constraints. The first indication that could eventually corroborate such an interpretation, once the observed common red spectrum is confirmed as a nHz gravitational wave background, could be the spectral tilt of the signal. In fact, the current data already show a very slight preference for a spectrum that is softer than what is expected from the leading astrophysical explanation.

A hidden self-interacting dark matter sector with first-order cosmological phase transition and gravitational wave

A hidden self-interacting dark matter sector with first-order cosmological phase transition and gravitational wave

Gravitational echoes of lepton number symmetry breaking with light and ultralight Majorons

We formulate a version of the low-scale Majoron model equipped with an inverse seesaw mechanism featuring lepton-number preserving dimension-6 operators in the scalar potential. Contrary to its dimension-4 counterpart, we find that the model can simultaneously provide light and ultralight Majorons, neutrino masses and their mixing, while featuring strong first-order cosmological phase transitions associated to the spontaneous breaking of the lepton number and the electroweak symmetries in the early Universe. We show by a detailed numerical analysis under which circumstances the model can be probed via the primordial gravitational wave spectrum potentially observable at LISA and other planned facilities. We discuss which implications result for collider physics observables, such as scalar trilinear couplings, the scalar mixing angle and the mass of a new CP-even Higgs boson.

511 keV line and primordial black holes from first-order phase transitions

511 keV gamma-ray excess from the Galactic center is a long lasting anomaly without satisfying astrophysical explanation. Hawking evaporation of hypothetical primordial black hole (PBH) with mass 1.0 × 10-17 ≲ M PBH/M ⊙ ≲ 8.0 × 10-17 and fractional abundance 10-3 ≲ f PBH ≲ 1.0, gives rise substantial non-relativistic electrons/positrons annihilating into diphoton, well reproduces the 511 keV line. However, it is obscure of the mechanism behind to form PBH with meteoritical mass in the early Universe. In this work, we investigated the production mechanism of PBHs through a cosmological first-order phase transition induced by quartic effective thermal potential via a scalar field in dark sector. We found the phase transition with vacuum energy, 𝒪(1) ≲ B 1/4/MeV ≲ 𝒪 (100), produces the desired monochromatic PBH mass and abundance fraction. Correlated signatures of gravitational wave and extragalactic gamma-ray, respectively coming from phase transition and black hole evaporation, are within μAres and AMEGO/e-ASTROGAM/COSI/XGIS-THESUS projected sensitivities. Finally, we include the PBH mass function from FOPT and found it can not improve the explanation to 511 keV excess.

Type Ia supernovae induced by primordial black holes from dark first-order phase transition

A primordial black hole (PBH) with mass 10−15≤MPBH/M⊙≤10−10 is currently beyond the sensitivity of both microlensing and black hole (BH) evaporation methods. A novel scenario has been proposed: When a PBH with mass 10−14≤MPBH/M⊙≤10−11 transits through a white dwarf (WD) made up of carbon and oxygen, Bondi-Hoyle-Lyttleton (BHL) accretion in a reactive medium creates a shock wave, which generates direct detonation ignition in the WD core and then leads to thermonuclear supernovae (SNe Ia). The aim of this study is to impose constraints on the PBH to dark matter (DM) abundance fraction, fPBH, via comparing the SN Ia event rates between PBH hypotheses and observational data. For PBH fraction less than unity, we found the observed event rate prefers PBH mass region, 7.6×10−13≤MPBH/M⊙≤6.1×10−12, under the Navarro–Frenk–White (NFW) profile. Meanwhile, the aforementioned PBH mass and abundance can be efficiently produced via a cosmological first-order phase transition (FOPT) in dark sector which associates with O(MeV) energy scale and thus gives rise to complementary signals of stochastic gravitational waves (GWs) with peak frequencies from 10−6 Hz to 10−5 Hz which can be probed by future μAres GW interferometer.

Model-dependent analysis method for energy budget of the cosmological first-order phase transition

The kinetic energy of the fluid shell in the cosmological first-order phase transition is crucial for predicting the gravitational wave signals generated by the sound wave mechanism. We propose a model-dependent method to calculate the kinetic energy fraction by dividing the bubble-fluid system into three distinct regions: the symmetric phase, the broken phase, and the bubble wall. By solving the local equation of motion of the scalar field with a phenomenological friction term, the bubble wall velocity and the boundary conditions of the fluid equations of both phases can be derived simultaneously. Then, for a given particle physics model, the fluid profiles of different hydrodynamical modes and the corresponding kinetic energy fraction can be obtained. Our method can also capture the temperature dependency of the sound speed of the plasma. Compared with the conventional model-independent method, our approach is based on an accurate equation of state derived directly from the effective potential and takes into account the contribution of the bubble wall to the energy-momentum tensor. Therefore, our method in-principle provides a more consistent and accurate result, which is crucial for high-precision calculations of the gravitational waves induced by the first-order phase transition.

Constraining the gravitational-wave spectrum from cosmological first-order phase transitions using data from LIGO-Virgo first three observing runs

We search for a first-order phase transition (PT) gravitational wave (GW) signal from Advanced LIGO and Advanced Virgo's first three observing runs. Due to the large theoretical uncertainties, four shapes of GW energy spectral from bubble and sound wave collisions widely adopted in literature are investigated, separately. Our results indicate that there is no evidence for the existence of such GW signals, and therefore we give the upper limits on the amplitude of GW energy spectrum Ωpt(f *) in the peak frequency range of f * ∈ [5,500] Hz for these four theoretical models, separately. We find that Ωpt(f * ≃ 40 Hz) < 1.3 × 10-8 at 95% credible level, and roughly H */β ≲ 0.1 and α ≲ 1 at 68% credible level in the peak frequency range of 20 ≲ f * ≲ 100 Hz corresponding to the mostsensitive frequency band of Advanced LIGO and Advanced Virgo's first three observing runs, where H * is the Hubble parameter when PT happens, β is the bubble nucleation rate and α is the normalized latent heat.

Boosted dark matter from primordial black holes produced in a first-order phase transition

During a cosmological first-order phase transition in a dark sector, fermion dark matter particles χ can form macroscopic Fermi balls that collapse to primordial black holes (PBHs) under certain conditions. The evaporation of the PBHs produces a boosted χ flux, which may be detectable if χ couples to visible matter. We consider the interaction of χ with electrons, and calculate signals of the dark matter flux in the XENON1T, XENONnT, Super-Kamiokande and Hyper-Kamiokande experiments. A correlated gravitational wave signal from the phase transition can be observed at THEIA and μAres. An amount of dark radiation measurable by CMB-S4 is an epiphenomenon of the phase transition.

Supercool subtleties of cosmological phase transitions

We investigate rarely explored details of supercooled cosmological first-order phase transitions at the electroweak scale, which may lead to strong gravitational wave signals or explain the cosmic baryon asymmetry. The nucleation temperature is often used in phase transition analyses, and is defined through the nucleation condition: on average one bubble has nucleated per Hubble volume. We argue that the nucleation temperature is neither a fundamental nor essential quantity in phase transition analysis. We illustrate scenarios where a transition can complete without satisfying the nucleation condition, and conversely where the nucleation condition is satisfied but the transition does not complete. We also find that simple nucleation heuristics, which are defined to approximate the nucleation temperature, break down for strong supercooling. Thus, studies that rely on the nucleation temperature — approximated or otherwise — may misclassify the completion of a transition. Further, we find that the nucleation temperature decouples from the progress of the transition for strong supercooling. We advocate use of the percolation temperature as a reference temperature for gravitational wave production, because the percolation temperature is directly connected to transition progress and the collision of bubbles. Finally, we provide model-independent bounds on the bubble wall velocity that allow one to predict whether a transition completes based only on knowledge of the bounce action curve. We apply our methods to find empirical bounds on the bubble wall velocity for which the physical volume of the false vacuum decreases during the transition. We verify the accuracy of our predictions using benchmarks from a high temperature expansion of the Standard Model and from the real scalar singlet model.

Higgsless simulations of cosmological phase transitions and gravitational waves

First-order cosmological phase transitions in the early Universe source sound waves and, subsequently, a background of stochastic gravitational waves. Currently, predictions of these gravitational waves rely heavily on simulations of a Higgs field coupled to the plasma of the early Universe, the former providing the latent heat of the phase transition. Numerically, this is a rather demanding task since several length scales enter the dynamics. From smallest to largest, these are the thickness of the Higgs interface separating the different phases, the shell thickness of the sound waves, and the average bubble size. In this work, we present an approach to perform Higgsless simulations in three dimensions, producing fully nonlinear results, while at the same time removing the hierarchically smallest scale from the lattice. This significantly reduces the complexity of the problem and contributes to making our approach highly efficient. We provide spectra for the produced gravitational waves for various choices of wall velocity and strength of the phase transition, as well as introduce a fitting function for the spectral shape.

Barrow entropy and stochastic gravitational wave background generated from cosmological QCD phase transition

In this work we investigate the stochastic gravitational wave background generated during the first-order cosmological QCD phase transition of the early universe in the framework of the Barrow entropy. We first derived the Barrow corrections to the expression of stochastic gravitational wave background spectrum in presence of trace anomaly. Then, by taking account of Bubble wall collisions, sound waves and magnetohydrodynamic turbulence as the sources of stochastic gravitational wave, an analysis of the influence of Barrow entropy on the total energy density and the peak signal of stochastic gravitational wave signal is carried out. Finally, we discuss the possibility of detectors for the detection of these stochastic gravitational wave signals. Our results show that effect of Barrow entropy plays an important role in the temporal evolution of temperature of the universe as a function of the Hubble parameter, which leads to the signal of stochastic gravitational wave to shift towards the lower frequency regime, making the signal of stochastic gravitational wave possible to be probed by relevant ongoing and upcoming gravitational waves experiments.

Constraining First-Order Phase Transitions with Curvature Perturbations.

The randomness of the quantum tunneling process induces superhorizon curvature perturbations during cosmological first-order phase transitions. We for the first time utilize curvature perturbations to constrain the phase transition parameters, and find that the observations of the cosmic microwave background spectrum distortion and the ultracompact minihalo abundance can give strict constraints on the phase transitions below 100GeV, especially for the low-scale phase transitions and some electroweak phase transitions. The current constraints on the phase transition parameters are largely extended by the results of this work, therefore provide an novel approach to probe related new physics.