Phase Transitions In Early Universe Research Articles

Evolution of current-carrying string networks

Cosmic string networks are expected to form in early Universe phase transitions via the Kibble mechanism and are unavoidable in several Beyond the Standard Model theories. While most predictions of observational signals of string networks assume featureless Abelian-Higgs or Nambu-Goto string networks, in many such extensions the networks can carry additional degrees of freedom, including charges and currents; these are often generically known as superconducting strings. All such degrees of freedom can impact the evolution of the networks and therefore their observational signatures. We report on the results of 20483 field theory simulations of the evolution of a current-carrying network of strings, highlighting the different scaling behaviours of the network in the radiation and matter eras. We also report the first numerical measurements of the coherence length scales for the charge and current and of the condensate equation of state, and show that the latter mainly depends on the expansion rate, with chirality occurring for the matter era. Qualitatively, the fact that the matter era is the optimal expansion rate for these networks to reach scaling is in agreement with recent analytic modelling.

Consequences of a stabilizing field’s self-interactions for RS cosmology

It has been argued that the Randall-Sundrum (RS) phase transition rate is suppressed when the holographic theory corresponds to a large N Yang-Mills and when the stabilizing field has a small mass. Here we argue that self-interactions can alleviate the latter suppression. We consider a cubic term in the bulk potential for the Goldberger-Wise (GW) scalar that is responsible for stabilizing the RS geometry. Adding a cubic term suffices to separate the two roles of the GW stabilization: generating a large hierarchy and triggering confinement. We study the resulting radion potential and the dynamics of the early universe phase transition. For a negative coefficient of the cubic term, the effect of the cubic becomes important in the infra-red, and the resulting radion potential is deeper, thereby increasing the radion mass while maintaining a large hierarchy. Staying within the radion effective field theory, we calculate the rate of bubble nucleation from the hot phase to the confined RS phase, both in thin and thick wall limits. The cubic term enhances the rate and allows relaxing the condition on the maximum number of colors Nmax of the dual theory for which the phase transition can be completed. Importantly, this reduces the amount of supercooling that the false vacuum undergoes, increases the peak frequency of the gravitational waves (GW) produced from bubble collisions, and reduces the strength of the GW signal. The reduced GW signal is however still within the reach of proposed space-based GW detectors.

Bubble nucleation at zero and nonzero temperatures

The theory of false vacuum decay in a thermal system may have a cross-over from predominantly thermal transitions to quantum transitions as the temperature is decreased. New numerical methods and results are presented here that can be used to model thermal and vacuum bubble nucleation in this regime for cosmology and for laboratory analogues of early universe phase transitions.

Probing early Universe supercooled phase transitions with gravitational wave data

We investigate the reach of the LIGO/Virgo/KAGRA detectors in the search for signatures of first-order phase transitions in the early Universe. Utilizing data from the first three observing runs, we derive constraints on the parameters of the underlying gravitational-wave background, focusing on transitions characterized by strong supercooling. As an application of our analysis, we determine bounds on the parameter space of two representative particle physics models. We also comment on the expected reach of third-generation detectors in probing supercooled phase transitions.

Decay of acoustic turbulence in two dimensions and implications for cosmological gravitational waves

Gravitational waves from a phase transition associated with the generation of the masses of elementary particles are within the reach of future space-based detectors such as LISA. A key determinant of the resulting power spectrum, not previously studied, is the lifetime of the acoustic turbulence which follows. We study decaying acoustic turbulence using numerical simulations of a relativistic fluid in two dimensions. Working in the limit of non-relativistic bulk velocities, with an ultra-relativistic equation of state, we find that the energy spectrum evolves towards a self-similar broken power law, with a high-wavenumber behaviour of $k^{-2.08 \pm 0.08}$, cut off at very high $k$ by the inverse width of the shock waves. Our model for the decay of acoustic turbulence can be extended to three dimensions using the universality of the high-$k$ power law and the evolution laws for the kinetic energy and the integral length scale. It is used to build an estimate for the gravitational wave power spectrum resulting from a collection of shock waves, as might be found in the aftermath of a strong first order phase transition in the early universe. The power spectrum has a peak wavenumber set by the initial length scale of the acoustic waves, and a new secondary scale at a lower wavenumber set by the integral scale after a Hubble time. Between these scales a distinctive new power law appears. Our results allow more accurate predictions of the gravitational wave power spectrum for a wide range of early universe phase transition scenarios.

Multitension strings in high-resolution U(1)×U(1) simulations

Topological defects are a fossil relic of early Universe phase transitions, with cosmic strings being the best motivated example. While in most cases one studies Nambu-Goto or Abelian-Higgs strings, one also expects that cosmologically realistic strings should have additional degrees of freedom in their worldsheets, one specific example being superstrings from Type IIB superstring theory. Here we continue the scientific exploitation of our recently developed multi-GPU field theory cosmic strings code to study the evolution of U(1)$\times$U(1) multitension networks, which are a numerically convenient proxy: these contain two lowest-tension strings networks able to interact and form bound states, providing a convenient first approximation to the behaviour expected from cosmic superstrings. (...) We rely on the largest field theory simulations of this model so far, specifically $4096^3$, $\Delta x = 0.5$ boxes. We present robust evidence of scaling for the lightest strings, measured through a complete and self-consistent set of correlation length and velocity diagnostics. We also find a linearly growing average length of the bound state segments, consistent with a scaling behaviour. (In previously reported lower-resolution simulations, such behaviour had only been identified with carefully engineered initial conditions, rich in those segments.) Finally, while we see no evidence of a large population of bound states forming at early stages of the network evolution, we do present tentative evidence for an asymptotic constant value of the fraction of bound states, with this value being different in the radiation and the matter eras. Our work demonstrates that our GPU-accelerated field theory code can by successfully extended beyond the simple Abelian-Higgs approximation, and enables future detailed studies of realistic string networks and of their observational signatures.

Bubble clustering in cosmological first order phase transitions

False vacuum decay in quantum mechanical first order phase transitions is a phenomenon with wide implications in cosmology and presents interesting theoretical challenges. In the standard approach, it is assumed that false vacuum decay proceeds through the formation of bubbles that nucleate at random positions in spacetime and subsequently expand. In this paper, we investigate the presence of correlations between bubble nucleation sites using a recently proposed semiclassical stochastic description of vacuum decay. This procedure samples vacuum fluctuations, which are then evolved using classical lattice simulations. We compute the two-point function for bubble nucleation sites from an ensemble of simulations, demonstrating that nucleation sites cluster in a way that is qualitatively similar to peaks in random Gaussian fields. We qualitatively assess the phenomenological implications of bubble clustering in early Universe phase transitions, which include features in the power spectrum of stochastic gravitational waves and an enhancement or suppression of the probability of observing bubble collisions in the eternal inflation scenario.

Simulating cosmological supercooling with a cold atom system. II. Thermal damping and parametric instability

We perform an analysis of the supercooled state in an analog of an early universe phase transition based on a one-dimensional, two-component Bose gas with time-dependent interactions. We demonstrate that the system behaves in the same way as a thermal, relativistic Bose gas undergoing a first-order phase transition. We propose a way to prepare the state of the system in the metastable phase as an analog to supercooling in the early universe. We show that parametric resonances in the system can be suppressed by thermal damping if the damping rate is similar to some of the higher rates previously used for modeling nonequilibrium experiments. However, the theoretically predicted damping rate for equilibrium systems within our model is too weak to suppress the resonances.

Bridging the gap: spectral distortions meet gravitational waves

ABSTRACT Gravitational waves (GWs) have the potential to probe the entirety of cosmological history due to their nearly perfect decoupling from the thermal bath and any intervening matter after emission. In recent years, GW cosmology has evolved from merely being an exciting prospect to an actively pursued avenue for discovery, and the early results are very promising. As we highlight in this paper, spectral distortions (SDs) of the cosmic microwave background (CMB) uniquely probe GWs over six decades in frequency, bridging the gap between astrophysical high- and cosmological low-frequency measurements. This means SDs will not only complement other GW observations, but will be the sole probe of physical processes at certain scales. To illustrate this point, we explore the constraining power of various proposed SD missions on a number of phenomenological scenarios: early-universe phase transitions (PTs), GW production via the dynamics of SU(2) and ultralight U(1) axions, and cosmic string (CS) network collapse. We highlight how some regions of parameter space were already excluded with data from COBE/FIRAS , taken over two decades ago. To facilitate the implementation of SD constraints in arbitrary models, we provide GW2SD. This tool calculates the window function, which easily maps a GW spectrum to an SD amplitude, thus opening another portal for GW cosmology with SDs, with wide reaching implications for particle physics phenomenology.

A real triplet-singlet extended Standard Model: dark matter and collider phenomenology

We examine the collider and dark matter phenomenology of the Standard Model extended by a hypercharge-zero SU(2) triplet scalar and gauge singlet scalar. In particular, we study the scenario where the singlet and triplet are both charged under a single ℤ2 symmetry. We find that such an extension is capable of generating the observed dark matter density, while also modifying the collider phenomenology such that the lower bound on the mass of the triplet is smaller than in minimal triplet scalar extensions to the Standard Model. A high triplet mass is in tension with the parameter space that leads to novel electroweak phase transitions in the early universe. Therefore, the lower triplet masses that are permitted in this extended model are of particular importance for the prospects of successful electroweak baryogenesis and the generation of gravitational waves from early universe phase transitions.

Simultaneous estimation of astrophysical and cosmological stochastic gravitational-wave backgrounds with terrestrial detectors

The recent Advanced LIGO and Advanced Virgo joint observing runs have not claimed a stochastic gravitational-wave background detection, but one expects this to change as the sensitivity of the detectors improves. The challenge of claiming a true detection will be immediately succeeded by the difficulty of relating the signal to the sources that contribute to it. In this paper, we consider backgrounds that comprise compact binary coalescences and additional cosmological sources, and we set simultaneous upper limits on these backgrounds. We find that the Advanced LIGO, Advanced Virgo network, operating at design sensitivity, will not allow for separation of the sources we consider. Third generation detectors, sensitive to most individual compact binary mergers, can reduce the astrophysical signal via subtraction of individual sources, and potentially reveal a cosmological background. Our Bayesian analysis shows that, assuming a detector network containing Cosmic Explorer and Einstein Telescope and reasonable levels of individual source subtraction, we can detect cosmological signals $\Omega_{\rm{CS}} (25\,\rm{Hz})=4.5 \times 10^{-13}$ for cosmic strings, and $\Omega_{\rm BPL}(25\,\rm{Hz})= 2.2 \times 10^{-13}$ for a broken power law model of an early universe phase transition.

Gravitational wave signatures of lepton universality violation

We analyze the prospects for using gravitational waves produced in early universe phase transitions as a complementary probe of the flavor anomalies in B meson decays. We focus on the Left-Right SU(4) Model, for which the strength of the observed lepton universality violation and consistency with other experiments impose a vast hierarchy between the symmetry breaking scales. This leads to a multipeaked gravitational wave signature within the reach of upcoming gravitational wave detectors.

Numerical analysis of the magnetogenesis from early universe phase transitions

AbstractWe present the results of General Relativistic Magnetohydrodynamic simulations utilizing initial conditions from both the Electroweak and Quantum Chromodynamic (QCD) phase transitions in order to determine if seed magnetic fields may be generated via the Biermann Battery Mechanism of Magnetogenesis. These simulations occur in a simulated early universe between 10−11 s and 103 s after the Big Bang. We find that magnetic fields greater than 10−20 G may be generated on the Mpc scale. This is believed to be strong enough to generate the large intergalactic magnetic fields seen today. Further work is needed to understand how these fields may have impacted the large‐scale structures we currently observe.

Simulating cosmological supercooling with a cold-atom system

We perform an analysis of the supercooled state in an analogue to an early universe phase transition based on a one dimensional, two-component Bose gas. We demonstrate that the thermal fluctuations in the relative phase between the components are characteristic of a relativistic thermal system. Furthermore, we demonstrate the equivalence of two different approaches to the decay of the metastable state: specifically a non-perturbative thermal instanton calculation and a stochastic Gross--Pitaevskii simulation.

Subtracting compact binary foreground sources to reveal primordial gravitational-wave backgrounds

Detection of primordial gravitational-wave backgrounds generated during the early universe phase transitions is a key science goal for future ground-based detectors. The rate of compact binary mergers is so large that their cosmological population produces a confusion background that could masquerade the detection of potential primordial stochastic backgrounds. In this paper we study the ability of current and future detectors to resolve the confusion background to reveal interesting primordial backgrounds. The current detector network of LIGO and Virgo and the upcoming KAGRA and LIGO-India will not be able to resolve the cosmological compact binary source population and its sensitivity to stochastic background will be limited by the confusion background of these sources. We find that a network of three (and five) third generation (3G) detectors of Cosmic Explorer and Einstein Telescope will resolve the confusion background produced by binary black holes leaving only about 0.013\% (respectively, 0.00075\%) unresolved; in contrast, as many as 25\% (respectively, 7.7\%) of binary neutron star sources remain unresolved. Consequently, the binary black hole population will likely not limit observation of primordial backgrounds but the binary neutron star population will limit the sensitivity of 3G detectors to $\Omega_{\rm GW} \sim 10^{-11}$ at 10 Hz (respectively, $\Omega_{\rm GW} \sim 3\times 10^{-12}$).

Probing cosmic strings with gravitational-wave fringe

Cosmic strings are important remnants of early-Universe phase transitions. We show that they can be probed by Gravitational Waves (GWs) from compact binary mergers. If such chirping GW passes by a cosmic string, it is gravitationally lensed and left with a characteristic signal of the lensing—the GW fringe. It is observable naturally through the frequency chirping of GWs. This allows to probe cosmic strings with small tension Δ = 8π G μ = 10−6 − 10−10, just below the current constraint, at high-frequency LIGO-band and mid-band detectors. Although its detection rates are estimated to be small, even a single detection can be used to identify a cosmic string. Contrary to the stochastic GW produced from loop decays only in local U(1) models, the GW fringe can directly probe straight strings model independently. This is also complementary to the existing probes with the strong lensing of light.

Symmetry Restoration and Breaking at Finite Temperature: An Introductory Review

Symmetries at finite temperature are of great importance to understand dynamics of spontaneous symmetry breaking phenomena, especially phase transitions in early Universe. Some symmetries such as the electroweak symmetry can be restored in hot environment. However, it is a nontrivial question that the phase transition occurs via first or second order, or even smooth crossover, which strongly depends on underlying physics. If it is first order, gravitational waves can be generated, providing a detectable signal of this epoch. Moreover, the baryon asymmetry of the Universe can also arise under some conditions. In this article, the electroweak phase transition is reviewed, focusing particularly on the case of the first-order phase transition. Much attention is paid to multi-step phase transitions in which additional symmetry breaking such as a spontaneous Z 2 breaking plays a pivotal role in broadening the possibility of the first-order electroweak phase transition. On the technical side, we review thermal resummation that mitigates a bad infrared behavior related to the symmetry restoration. In addition, gauge and scheme dependences of perturbative calculations are also briefly discussed.

Gravitational waves from first order cosmological phase transitions in the Sound Shell Model

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 detonations, but the total power for deflagrations is predicted higher than numerical simulations show, indicating refinement of the model of the transfer of energy to the fluid is needed for accurate computations. We show how the time-dependence of the bubble nucleation rate affects the shape of the power spectrum: an exponentially rising nucleation rate produces higher amplitude gravitational waves at a longer wavelength than simultaneous nucleation. We present an improved fit for the predicted gravitational wave power spectrum in the form of a double broken power law, where the two breaks in the slope happen at wavenumber corresponding to the mean bubble separation and the thickness of the fluid shell surrounding the expanding bubbles, which in turn is related to the difference of the phase boundary speed from the speed of sound.

Hearing the echoes of electroweak baryogenesis with gravitational wave detectors

We report on the first joint analysis of observational signatures from the electroweak baryogenesis in both gravitational wave (GW) detectors and particle colliders. With an effective extension of the Higgs sector in terms of the dimension-6 operators, we derive a strong first-order phase transition in associated with a sizable CP violation to realize a successful electroweak baryogenesis. We calculate the GW spectrum resulting from the bubble nucleation, plasma transportation, and magnetohydrodynamic turbulence of this process that occurred after the big bang, and find that it yields GW signals testable in Evolved Laser Interferometer Space Antenna, Deci-hertz Interferometer Gravitational wave Observatory and Big Bang Observer. We further identify collider signals from the same mechanism that are observable at the planning Circular Electron Positron Collider. Our analysis bridges astrophysics/cosmology with particle physics by providing significant motivation for searches for GW event peaking at the $(10^{-4}, 1)$ Hz range, which are associated with signals at colliders, and highlights the possibility of an interdisciplinary observational window into baryogenesis. The technique applied in analyzing early universe phase transitions may enlighten the study of phase transitions in applied science.

Relic Entropy Growth and Initial Big Bang Conditions, as a Subset of Quantum Information

This paper shows how increased entropy values from an initially low big bang level can be measured experimentally by counting relic gravitons. Furthermore the physical mechanism of this entropy increase is explained via analogies with early-universe phase transitions. The role of Ng’s revised infinite quantum statistics in the physics of gravitational wave detection is acknowledged. Ng’s infinite quantum statistics can be used to show that is a starting point to the increasing net universe cosmological entropy. Finally, in a nod to similarities with zero point energy (ZPE) analysis, it is important to note that the resulting in fact is much lower, allowing for evaluating initial graviton production as an emergent field phenomena, which may be similar to how ZPE states can be used to extract energy from a vacuum if entropy is not maximized. The rapid increase in entropy so alluded to without near sudden increases to 1088 may be enough to allow successful modeling of relic graviton production for entropy in a manner similar to zero point energy (ZPE) energy extraction from a vacuum state. This entropy count is akin to quantum information models used to tell how much “information” may be stored in initial conditions, and transferred from a prior to the present