Cosmological Phase Transitions Research Articles

Flow-based nonperturbative simulation of first-order phase transitions

We present a flow-based method for simulating and calculating nucleation rates of first-order phase transitions in scalar field theory on a lattice. Motivated by recent advancements in machine learning tools, particularly normalizing flows for lattice field theory, we propose the “partitioning flow-based Markov chain Monte Carlo (PFMCMC) sampling” method to address two challenges encountered in normalizing flow applications for lattice field theory: the “mode-collapse” and “rare-event sampling” problems. Using a (2+1)-dimensional real scalar model as an example, we demonstrate the effectiveness of our PFMCMC method in modeling highly hierarchical order parameter probability distributions and simulating critical bubble configurations. These simulations are then used to facilitate the calculation of nucleation rates. We anticipate the application of this method to (3+1)-dimensional theories for studying realistic cosmological phase transitions.

Gravitational waves from first-order phase transitions in LISA: reconstruction pipeline and physics interpretation

We develop a tool for the analysis of stochastic gravitational wave backgrounds from cosmological first-order phase transitions with LISA: we initiate a template databank for these signals, prototype their searches, and forecast their reconstruction.The templates encompass the gravitational wave signals sourced by bubble collisions, sound waves and turbulence. Accounting for Galactic and extra-Galactic foregrounds, we forecast the region of the parameter space that LISA will reconstruct with better than ∼ 10% accuracy, if certain experimental and theoretical uncertainties are solved by the time LISA flies.We illustrate the accuracy with which LISA can reconstruct the parameters on a few benchmark signals, both in terms of the template parameters and the phase transition ones.To show the impact of the forecasts on physics beyond the Standard Model, we map the reconstructed benchmark measurements into the parameter spaces of the singlet extension of the Standard Model and of the classically conformal invariant U(1) B-L model.

Ladder top-quark condensation imprints in supercooled electroweak phase transition

The electroweak (EW) phase transition in the early Universe might be supercooled due to the presence of the classical scale invariance involving Beyond the Standard Model (BSM) sectors and the supercooling could persist down till a later epoch around which the QCD chiral phase transition is supposed to take place. Since this supercooling period keeps masslessness for all the six SM quarks, it has simply been argued that the QCD phase transition is the first order, and so is the EW one. However, not only the QCD coupling but also the top Yukawa and the Higgs quartic couplings get strong at around the QCD scale due to the renormalization group running, hence this scenario is potentially subject to a rigorous nonperturbative analysis. In this work, we employ the ladder Schwinger-Dyson (LSD) analysis based on the Cornwall-Jackiw-Tomboulis formalism at the two-loop level in such a gauge-Higgs-Yukawa system. We show that the chiral broken QCD vacuum emerges with the nonperturbative top condensate and the lightness of all six quarks is guaranteed due to the accidental U(1) axial symmetry presented in the top-Higgs sector. We employ a quark-meson model-like description in the mean field approximation to address the impact on the EW phase transition arising due to the top quark condensation at the QCD phase transition epoch. In the model, the LSD results are encoded to constrain the model parameter space. We then observe the cosmological phase transition of the first-order type and discuss the induced gravitational wave (GW) productions. We find that in addition to the conventional GW signals sourced from an expected BSM at around or over the TeV scale, the dynamical topponium-Higgs system can yield another power spectrum sensitive to the BBO, LISA, and DECIGO, etc.

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

Axion relic pockets — a theory of dark matter

We propose a new theory of dark matter based on axion physics and cosmological phase transitions. We show that theories in which a gauge coupling increases through a first-order phase transition naturally result in ‘axion relic pockets’: regions of relic false vacua stabilised by the pressure from a kinematically trapped, hot axion gas. Axion relic pockets provide a viable and highly economical theory of dark matter: the macroscopic properties of the pockets depend only on a single parameter (the phase transition temperature). We describe the formation, evolution and present-day properties of axion relic pockets, and outline how their phenomenology is distinct from existing dark matter paradigms. We briefly discuss how laboratory experiments and astronomical observations can be used to test the theory, and identify gamma-ray observations of magnetised, dark-matter-dense environments as particularly promising.

Cosmological tests of the dark energy models in Finsler-Randers space-time

The Finsler-Randers space-time offers a novel perspective on cosmic dynamics, departing from the constraints of General Relativity. This paper thoroughly investigates two dark energy models resulting from the parametrization of H within this geometric framework. We have conducted some geometrical and physical analysis of the dark energy models in Finslerian geometry. First, we have derived the field equations governing the universe's evolution within the Finsler-Randers formalism, incorporating the presence of dark energy. Through this, we explore its implications on cosmological phenomena, including cosmic expansion, late-time behavior of the universe, cosmological phase transition, and a few more. Also, we employ observational data such as Cosmic Chronometer, Supernovae, Gamma-Ray Bursts, Quasar, and baryon acoustic oscillations to constrain the parameters associated with dark energy in the Finsler-Randers universe. Comparing theoretical predictions with empirical observations, we assess the model viability and discern any deviations from the standard ΛCDM cosmology. Our findings offer intriguing insights into the nature of dark energy within this alternative gravitational framework, providing a deeper understanding of its role in shaping cosmic evolution. The implications of our results extend to fundamental cosmology, hinting at new avenues for research to unravel the mysteries surrounding dark energy and the geometric structure of the universe within non-standard gravitational theories.

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

A single-bubble source for gravitational waves in a cosmological phase transition

Abstract We show that quantum fluctuations of an expanding phase transition bubble give rise to gravitational wave (GW) emission, even when considering a single bubble, without bubble collisions or plasma effects. The ratio of GW energy to the total bubble energy reservoir increases with time as ∝ t. If the bubble expands for long enough before percolation destroys it, back-reaction due to the GW emission becomes important after t br ~ (16π5)m pl 2 R 0 3, where R 0 is the bubble nucleation radius and m pl is the reduced Planck mass. As seen by experiments today, the GW energy spectrum would appear blue. However, simple estimates suggest that the signal falls short of detection by even ambitious future experiments.

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

Particle shells from relativistic bubble walls

Relativistic bubble walls from cosmological phase transitions (PT) necessarily accumulate expanding shells of particles. We systematically characterize shell properties, and identify and calculate the processes that prevent them from free streaming: phase-space saturation effects, out-of-equilibrium 2 → 2 and 3 → 2 shell-shell and shell-bath interactions, and shell interactions with bubble walls. We find that shells do not free stream in scenarios widely studied in the literature, where standard predictions will need to be reevaluated, including those of bubble wall velocities, gravitational waves (GW) and particle production. Our results support the use of bulk-flow GW predictions in all regions where shells free stream, irrespectively of whether or not the latent heat is mostly converted in the scalar field gradient.

Scaling solutions for current-carrying cosmic string networks

Cosmic string networks are the best motivated relics of cosmological phase transitions, being unavoidable in many physically plausible extensions of the Standard Model. Most studies, including those providing constraints from and forecasts of their observational signals, rely on assumptions of featureless networks, neglecting the additional degrees of freedom on the string worldsheet, e.g., charges and currents, which are all but unavoidable in physically realistic models. An extension of the canonical velocity-dependent one-scale model, accounting for all such possible degrees of freedom, has been recently developed. Here we improve its physical interpretation by studying and classifying its possible asymptotic scaling solutions, and in particular how they are affected by the expansion of the Universe and the available energy loss or transfer mechanisms. We find three classes of solutions. For sufficiently fast expansion rates the charges and currents decay and one asymptotes to the Nambu-Goto case, while for slower expansion rates they can dominate the network dynamics. In between the two there is a third regime in which the network, including its charge and current, reaches full scaling. Under specific but plausible assumptions, this intermediate regime corresponds to the matter-dominated era. Our results agree with, and significantly extend, those of previous studies. Published by the American Physical Society 2024

Impact of theoretical uncertainties on model parameter reconstruction from GW signals sourced by cosmological phase transitions

Different computational techniques for cosmological phase transition parameters can impact the gravitational wave (GW) spectra predicted in a given particle physics model. To scrutinize the importance of this effect, we perform large-scale parameter scans of the dynamical real-singlet extended Standard Model using three perturbative approximations for the effective potential; the MS¯ and on shell schemes at leading order, and three-dimensional thermal effective theory (3D EFT) at next-to-leading order. While predictions of GW amplitudes are typically unreliable in the absence of higher-order corrections, we show that the reconstructed model parameter spaces are robust up to a few percent in uncertainty. While 3D EFT is accurate from one-loop order, theoretical uncertainties of reconstructed model parameters, using four-dimensional standard techniques, remain dominant over the experimental ones even for signals merely strong enough to claim a detection by LISA. Published by the American Physical Society 2024

Dark matter production accompanied by gravitational wave signals during cosmological phase transitions

We investigate the temperature-dependent production of feebly interacting massive dark matter particle (FIMP DM) within a Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_2$$\\end{document} model, incorporating two Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_2$$\\end{document}-odd scalar fields. In specific parameter regions, three distinct mechanisms individually dominate the production of the FIMP DM. These mechanisms include the semi-production process, commonly known as the “exponential growth” process, the three-body decay process, and the production from pair annihilations of the bath particles. It is crucial to consider the thermal history during the evolution of FIMPs, as it involves multiple phase transitions occurring prior to the freeze-in of dark matter. Consequently, the scalar masses experience thermal variations, leading to distinctive evolutionary trajectories for FIMPs when compared to scenarios without accounting for the thermal effects. Notably, the unique patterns of FIMP evolution are accompanied by the production of gravitational waves, presenting promising opportunities for detection using forthcoming interferometers.

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.

Dark radiation isocurvature from cosmological phase transitions

Cosmological first order phase transitions are typically associated with physics beyond the Standard Model, and thus of great theoretical and observational interest. Models of phase transitions where the energy is mostly converted to dark radiation can be constrained through limits on the dark radiation energy density (parameterized by ΔN eff). However, the current constraint (ΔN eff < 0.3) assumes the perturbations are adiabatic. We point out that a broad class of non-thermal first order phase transitions that start during inflation but do not complete until after reheating leave a distinct imprint in the scalar field from bubble nucleation. Dark radiation inherits the perturbation from the scalar field when the phase transition completes, leading to large-scale isocurvature that would be observable in the CMB. We perform a detailed calculation of the isocurvature power spectrum and derive constraints on ΔN eff based on CMB+BAO data. For a reheating temperature of T rh and a nucleation temperature T *, the constraint is approximately ΔN eff ≲ 10-5 (T */T rh)-4, which can be much stronger than the adiabatic result. We also point out that since perturbations of dark radiation have a non-Gaussian origin, searches for non-Gaussianity in the CMB could place a stringent bound on ΔN eff as well.

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

Cosmological FLRW phase transitions and micro-structure under Kaniadakis statistics

This article studies the thermodynamics phase transitions and critical phenomena of an FLRW cosmological model under truncated Kaniadakis's statistics. The EoS is derived from the corrected Friedmann field equations and the thermodynamics unified first law. To approach thermodynamics, we use an approximation for KSAH≪1, on the cosmological equation, and also check the validity of our approximation. Then for different values from Kaniadakis parameter K, order O(10−37) for the relic-abundance, O(10−84) for 7Li-abundance and O(10−125) in the recombination era, the EoS reveals non-trivial critical points where a first-order phase transition occurs a sort of a van der Waals fluid. Interestingly, the numerical values of the critical exponents are the same as those of the van der Waals system. Besides, to obtain more insights into the thermodynamics description, the so-called Ruppeiner's geometry is studied through the normalized scalar curvature, disclosing this invariant zone where the system undergoes repulsive/attractive interactions. Near the critical point, this curvature provides again the same critical exponent and universal constant value as for van der Waals fluid. Despite the similarity, both systems are quite different because the present one considers a relativistic entropy (Kaniadakis entropy) while the Van der Waals gas responds to a classical entropy (Maxwell-Boltzmann).

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.