Cosmological First-order Phase Transition Research Articles

Hydrodynamic stability of cosmological quark-hadron phase transitions

Recent results from linear perturbation theory suggest that first-order cosmological quark-hadron phase transitions occurring as deflagrations may be ``borderline'' unstable, and those occurring as detonations may give rise to growing modes behind the interface boundary. However, since nonlinear effects can play important roles in the development of perturbations, unstable behavior cannot be asserted entirely by linear analysis, and the uncertainty of these recent studies is compounded further by nonlinearities in the hydrodynamics and self-interaction fields. In this paper we investigate the growth of perturbations and the stability of quark-hadron phase transitions in the early Universe by solving numerically the fully nonlinear relativistic hydrodynamics equations coupled to a scalar field with a quartic self-interaction potential regulating the transitions. We consider single, perturbed, phase transitions propagating either by detonation or deflagration, as well as multiple phase and shock front interactions in 1+2 dimensional spacetimes.

Defect formation rates in cosmological first-order phase transitions

In cosmological first-order phase transitions, the progress of true-vacuum bubbles is expected to be significantly retarded by the interaction between the bubble wall and the hot plasma. It has been claimed that this leads to a significant reduction in the number of topological defects formed per bubble, as a result of phase equilibration between bubbles. This claim has been verified for spontaneously-broken global symmetries. We perform a series of simulations of complete phase transitions in the 2+1-dimensional U(1)-Abelian Higgs model, for a range of bubble wall velocities, in order to obtain a quantitative measure of the effect of bubble wall speed on the number density of topological defects. We find that the number of defects formed is i) significantly lower in the local than the global case and ii) decreases exponentially as a function of wall velocity. Slow-moving bubbles also lead, however, to the nucleation of more bubbles before the phase transition is complete. Our simulations show that this is in fact the dominant effect, and so we predict {\em more} defects per unit volume as a result of the sub-luminal bubble wall terminal velocity.

Nontopological solitons as nucleation sites for cosmological phase transitions

I consider quantum field theories that admit charged non-topological solitons of the Q-ball type, and use the fact that in a first-order cosmological phase transition, below the critical temperature, there is a value of the soliton charge above which the soliton becomes unstable and expands, converting space to the true vacuum, much like a critical bubble in the case of ordinary tunneling. Using a simple model for the production rate of Q-balls through charge accretion during a random walk out of equilibrium, I calculate the probability for the formation of critical charge solitons and estimate the amount of supercooling needed for the phase transition to be completed.

Cosmological consequences of slow-moving bubbles in first-order phase transitions

In cosmological first-order phase transitions, the progress of true-vacuum bubbles is expected to be significantly retarded by the interaction between the bubble wall and the hot plasma. We examine the evolution and collision of slow-moving true-vacuum bubbles. Our lattice simulations indicate that phase oscillations, predicted and observed in systems with a local symmetry and with a global symmetry where the bubbles move at speeds less than the speed of light, do not occur inside collisions of slow-moving local-symmetry bubbles. We observe almost instantaneous phase equilibration which would lead to a decrease in the expected initial defect density, or possibly prevent defects from forming at all. We illustrate our findings with an example of defect formation suppressed in slow-moving bubbles. Slow-moving bubble walls also prevent the formation of `extra defects', and in the presence of plasma conductivity may lead to an increase in the magnitude of any primordial magnetic field formed.

Stability of cosmological detonation fronts.

We present results of a linear stability analysis of relativistic detonation fronts, which have been considered as representing phase interfaces in cosmological first-order phase transitions. After discussing general stability conditions for detonation fronts, we concentrate on the properties of the fronts with respect to corrugation instabilities and discuss separately the cases of Chapman-Jouguet and strong detonation waves. Contrary to what is recently claimed, we find that strong detonations are both evolutionary and stable with respect to corrugations of the front. Moreover, Chapman-Jouguet detonations appear to be unconditionally linearly stable. The implications of the stability results for first-order cosmological phase transitions are presented and a discussion of the causal structure of reaction fronts is also given.

Large scale inhomogeneities from the QCD phase transition.

We examine the first-order cosmological QCD phase transition for a large class of parameter values, previously considered unlikely. We find that the hadron bubbles can nucleate at very large distance scales, they can grow as detonations as well as deflagrations, and that the phase transition may be completed without reheating to the critical temperature. For a subset of the parameter values studied, the inhomogeneities generated at the QCD phase transition might have a noticeable effect on nucleosynthesis.

Exact critical bubble free energy and the effectiveness of effective potential approximations.

To calculate the temperature at which a first-order cosmological phase transition occurs, one must calculate $F_c(T)$, the free energy of a critical bubble configuration. $F_c(T)$ is often approximated by the classical energy plus an integral over the bubble of the effective potential; one must choose a method for calculating the effective potential when $V''<0$. We test different effective potential approximations at one loop. The agreement is best if one pulls a factor of $\mu^4/T^4$ into the decay rate prefactor [where $\mu^2 = V''(\phi_f)$], and takes the real part of the effective potential in the region $V''<0$. We perform a similar analysis on the 1-dimensional kink.

Growth of bubbles in cosmological phase transitions.

We study how bubbles grow after the initial nucleation event in generic first-order cosmological phase transitions characterized by the values of the latent heat $L$, interface tension $\ensuremath{\sigma}$, and correlation length $\ensuremath{\xi}$, and driven by a scalar order parameter $\ensuremath{\varphi}$. Equations coupling $\ensuremath{\varphi}(t,\mathbf{x})$ and the fluid variables $\mathbf{v}(t,\mathbf{x})$, $T(t,\mathbf{x})$ and depending on a dissipative constant $\ensuremath{\Gamma}$ are derived and solved numerically in the (1+1)-dimensional case starting from a slightly deformed critical bubble configuration $\ensuremath{\varphi}(0,\mathbf{x})$. The parameters $L$, $\ensuremath{\sigma}$, $\ensuremath{\xi}$ corresponding to QCD and electroweak phase transitions are chosen and the whole history of the bubble with the formation of combustion and shock fronts is computed as a function of $\ensuremath{\Gamma}$. Both deflagrations and detonations can appear depending on the values of the parameters. Reheating due to collisions of bubbles is also computed.

Gravitational radiation from first-order phase transitions.

We consider the stochastic background of gravity waves produced by first-order cosmological phase transitions from two types of sources: colliding bubbles and hydrodynamic turbulence. First we discuss the fluid mechanics of relativistic spherical combustion. We then numerically collide many bubbles expanding at a velocity $v$ and calculate the resulting spectrum of gravitational radiation in the linearized gravity approximation. Our results are expressed as simple functions of the mean bubble separation, the bubble expansion velocity, the latent heat, and the efficiency of converting latent heat to kinetic energy of the bubble walls. A first-order phase transition is also likely to excite a Kolmogoroff spectrum of turbulence. We estimate the gravity waves produced by such a spectrum of turbulence and find that the characteristic amplitude of the gravity waves produced is comparable to that from bubble collisions. Finally, we apply these results to the electroweak transition. Using the one-loop effective potential for the minimal electroweak model, the characteristic amplitude of the gravity waves produced is $h\ensuremath{\simeq}1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}27}$ at a characteristic frequency of 4.1 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}3}$ Hz corresponding to $\ensuremath{\Omega}\ensuremath{\sim}{10}^{\ensuremath{-}22}$ in gravity waves, far too small for detection. Gravity waves from more strongly first-order phase transitions, including the electroweak transition in nonminimal models, have better prospects for detection, though probably not by LIGO.

Dynamics of cosmological phase transitions: Metastability revisited

The dynamics of first-order cosmological phase transitions is critically examined. In particular, criteria to estimate the strength of the transition are introduced. It is shown that for sufficiently weak transitions, thermal fluctuations away from the symmetric phase can efficiently populate the asymmetric phase at the critical temperature, leading to a mixing of the phases and to a different mechanism for the completion of the transition. These criteria are applied to the standard model electroweak phase transition.

Gravitational waves from first-order cosmological phase transitions.

A first-order cosmological phase transition that proceeds through the nucleation and collision of true-vacuum bubbles is a potent source of gravitational radiation. Possibilities for such include first-order inflation, grand-unified-theory-symmetry breaking, and electroweak-symmetry breaking. We have calculated gravity-wave production from the collision of two scalar-field vacuum bubbles, and, using an approximation based upon these results, from the collision of 20 to 30 vacuum bubbles. We present estimates of the relic background of gravitational waves produced by a first-order phase transition.

Bubble nucleation in first-order inflation and other cosmological phase transitions.

We address in some detail the kinematics of bubble nucleation and percolation in first-order cosmological phase transitions, with the primary focus on first-order inflation. We study how a first-order phase transition completes, describe measures of its progress, and compute the distribution of bubble sizes. For example, we find that the typical bubble size in a successful transition is of order 1% to 100% of the Hubble radius, and depends very weakly on the energy scale of the transition. We derive very general conditions that must be satisfied by \ensuremath{\Gamma}/${\mathit{H}}^{4}$ to complete the phase transition (\ensuremath{\Gamma}=bubble nucleation rate per unit volume; H=expansion rate; physically, \ensuremath{\Gamma}/${\mathit{H}}^{4}$ corresponds to the volume fraction of space occupied by bubbles nucleated over a Hubble time). In particular, \ensuremath{\Gamma}/${\mathit{H}}^{4}$ must exceed 9/4\ensuremath{\pi} to successfully end inflation. To avoid the deleterious effects of bubbles nucleated early during inflation on primordial nucleosynthesis and on the isotropy and spectrum of the cosmic microwave background radiation, during most of inflation \ensuremath{\Gamma}/${\mathit{H}}^{4}$ must be less than order ${10}^{\mathrm{\ensuremath{-}}4}$--${10}^{\mathrm{\ensuremath{-}}3}$. Our constraints imply that in a successful model of first-order inflation the phase transition must complete over a period of at most a few Hubble times and all but preclude individual bubbles from providing an interesting source of density perturbation. We note, though, that it is just possible for Poisson fluctuations in the number of moderately large-size bubbles to lead to interesting isocurvature perturbations, whose spectrum is not scale invariant. Finally, we analyze in detail several recently proposed models of first-order inflation.

Nucleation and bubble growth in a first-order cosmological electroweak phase transition.

We study the kinetics of first-order cosmological phase transitions assuming a four-parameter form for the Higgs potential driving the transition. This leads to a phenomenological equation of state for electroweak matter with a stable high-$T$ phase for $Tg{T}_{c}$ and a low-$T$ phase for $Tl{T}_{c}$. The nucleation probability of low-$T$ bubbles, both critical and subcritical, is computed and their growth and coalescence is simulated. We show that they can grow as deflagrations and that detonations are unlikely. Possible front velocities and entropy production are studied. The results are applied to parameter values conjectured for the electroweak phase transition and compared with those obtained for the quark\ensuremath{\rightarrow}hadron phase transition.

Fundamental constants and higher-dimensional universe

In order to study the origin of the fundamental constants and Dirac's large number, a cosmological solution in vacuum is presented in a seven-dimensional universe which is defined by adding extra three coordinates (e2G/c4)1/2, (hG/c3)1/2 and (Gm/c2) to the four-dimensional spacetime coordinates. It has common features with Chodos-Detweiler's solution. The parameters appearing in this theory are estimated to meet the conditions required by the cosmological first-order phase transition and Dirac's large number hypothesis.

Preon model and cosmological quantum-hyperchromodynamic phase transition.

From the cosmological viewpoint, we investigate whether or not recent preon models are compatible with the picture of the first-order phase transition from the preon phase to the composite quark-lepton phase. It is shown that the current models accepting the 't Hooft anomaly-matching condition together with quantum hyperchromodynamics are consistent with the cosmological first-order phase transition.

Magnetohydrodynamic Effects of a First-Order Cosmological Phase Transition

The author analyzes the spectrum, amplitude, and evolution of a tangled primeval magnetic field generated by macroscopic dynamo activity arising during a first-order phase transition in the early universe. The effects of the field on the matter distribution at late times could be much larger than that of the adiabatic or isothermal density fluctuations generated by the transition. With optimistic assumptions, magnetic fields generated during a transition at $T\ensuremath{\sim}0.2$ GeV could lead to the collapse of gas clouds of $\ensuremath{\simeq}{10}^{1\ensuremath{-}5}{M}_{\ensuremath{\bigodot}}$ after recombination, and to the formation of pregalactic stars or quasars.

Abundance of Primordial Holes Produced by Cosmological First-Order Phase Transition

One important prediction of a cosmological model based on grand unified theories is the production of primordial black holes and wormholes through a first· order phase transition. In this paper we estimate the abundance of these holes and their effects on cosmology. We show that they play several important roles in the subsequent evolution of the universe and that the observational information of the present universe, conversely, yields constraints on the phenomenological parameters in grand unified theories. Especially we find that both the thermal and quantum nucleations of vacuum bubbles are the necessary ingredients in construct· ing a cosmological model consistent with the present observations.

Evaporation of a Bubble Created by the Cosmological First-Order Phase Transition

Evaporation of a Bubble Created by the Cosmological First-Order Phase Transition

Creation of Schwarzschild-de Sitter wormholes by a cosmological first-order phase transition

It has been pointed out that the universe may contain Schwarzschild wormholes produced by first-order phase transitions of a vacuum. In this letter, we consider this possibility for the more general case in which the vacuum energy density inside growing bubbles remains finite. We show that (1) Schwarzschild-de Sitter wormholes are created instead of simple Schwarzschild ones, and (2) if the remaining vacuum energy density is greater than a critical value, no wormholes are created.

Cosmological first-order phase transition and the gravitational coupling of the scalar field

The tunneling probability of a possible first-order phase transition of the grand unification symmetry is calculated taking the running nature of the gauge coupling constant and the effect of the spacetime curvature into account. The transition should either occur at ∼10 10 GeV or never occur, depending crucially on the parameter characterizing the gravitational coupling of the scalar field.