In a cosmological first-order phase transition, bubbles of the stable phase nucleate and expand in the supercooled metastable phase. In many cases, the growth of bubbles reaches a stationary state, with bubble walls propagating as detonations or deflagrations. However, these hydrodynamical solutions may be unstable under corrugation of the interface. Such instability may drastically alter some of the cosmological consequences of the phase transition. Here, we study the hydrodynamical stability of deflagration fronts. We improve upon previous studies by making a more careful and detailed analysis. In particular, we take into account the fact that the equation of motion for the phase interface depends separately on the temperature and fluid velocity on each side of the wall. Fluid variables on each side of the wall are similar for weakly first-order phase transitions, but differ significantly for stronger phase transitions. As a consequence, we find that, for large enough supercooling, any subsonic wall velocity becomes unstable. Moreover, as the velocity approaches the speed of sound, perturbations become unstable on all wavelengths. For smaller supercooling and small wall velocities, our results agree with those of previous works. Essentially, perturbations on large wavelengths are unstable, unless the wall velocity is higher than a critical value. We also find a previously unobserved range of marginally unstable wavelengths. We analyze the dynamical relevance of the instabilities, and we estimate the characteristic time and length scales associated to their growth. We discuss the implications for the electroweak phase transition and its cosmological consequences.Comment: 45 pages, 13 figures. v2: Minor corrections, references added. v3: Typos corrected, minor modifications and references added (version accepted in PRD

Although inflation is a natural candidate to generate the lengths of coherence of magnetic fields needed to explain current observations, it needs to break conformal invariance of electromagnetism to obtain significant magnetic amplitudes. Of the simplest realizations are the kinetically-coupled theories $f^2(\phi)F_{\mu\nu}F^{\mu\nu}$ (or $IFF$ theories). However, these are known to suffer from electric fields backreaction or the strong coupling problem. In this work we shall confirm that such class of theories are problematic to support magnetogenesis during inflationary cosmology. On the contrary, we show that a bouncing cosmology with a contracting phase dominated by an equation of state with $p>-\rho/3$ can support magnetogenesis, evading the {backreaction/strong-coupling problem}. Finally, we study safe magnetogenesis in a particular bouncing model with an ekpyrotic-like contracting phase. In this case we found that $f^2(\phi)F^2$-instabilities might arise during the final kinetic-driven expanding phase for steep ekpyrotic potentials.Comment: 33 pages, 7 figures, v2: references added, typos corrected, v3 Final version published in NP

The steady state propagation of a phase transition front is classified, according to hydrodynamics, as a deflagration or a detonation, depending on its velocity with respect to the fluid. These propagation modes are further divided into three types, namely, weak, Jouguet, and strong solutions, according to their disturbance of the fluid. However, some of these hydrodynamic modes will not be realized in a phase transition. One particular cause is the presence of instabilities. In this work we study the linear stability of weak detonations, which are generally believed to be stable. After discussing in detail the weak detonation solution, we consider small perturbations of the interface and the fluid configuration. When the balance between the driving and friction forces is taken into account, it turns out that there are actually two different kinds of weak detonations, which behave very differently as functions of the parameters. We show that the branch of stronger weak detonations are unstable, except very close to the Jouguet point, where our approach breaks down.Comment: 34 pages, 11 figures. v2: typos corrected and minor change

We study statistical relationships between bubble walls in cosmological first-order phase transitions. We consider the conditional and joint probabilities for different points on the walls to remain uncollided at given times. We use these results to discuss space and time correlations of bubble walls and their relevance for the consequences of the transition. In our statistical treatment, the kinematics of bubble nucleation and growth is characterized by the nucleation rate and the wall velocity as functions of time. We obtain general expressions in terms of these two quantities, and we consider several specific examples and applications.

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 bubble collision mechanism.

This is the first in a series of papers where we study the dynamics of a bubble wall beyond usual approximations, such as the assumptions of spherical bubbles and infinitely thin walls. In this paper, we consider a vacuum phase transition. Thus, we describe a bubble as a configuration of a scalar field whose equation of motion depends only on the effective potential. The thin-wall approximation allows obtaining both an effective equation of motion for the wall position and a simplified equation for the field profile inside the wall. Several different assumptions are involved in this approximation. We discuss the conditions for the validity of each of them. In particular, the minima of the effective potential must have approximately the same energy, and we discuss the correct implementation of this approximation. We consider different improvements to the basic thin-wall approximation, such as an iterative method for finding the wall profile and a perturbative calculation in powers of the wall width. We calculate the leading-order corrections. Besides, we derive an equation of motion for the wall without any assumptions about its shape. We present a suitable method to describe arbitrarily deformed walls from the spherical shape. We consider concrete examples and compare our approximations with numerical solutions. In subsequent papers, we shall consider higher-order finite-width corrections, and we shall take into account the presence of the fluid.

The subsonic expansion of bubbles in a strongly first-order electroweak phase transition is a convenient scenario for electroweak baryogenesis. For most extensions of the Standard Model, stationary subsonic solutions (i.e., deflagrations) exist for the propagation of phase transition fronts. However, deflagrations are known to be hydrodynamically unstable for wall velocities below a certain critical value. We calculate this critical velocity for several extensions of the Standard Model and compare with an estimation of the wall velocity. In general, we find a region in parameter space which gives stable deflagrations as well as favorable conditions for electroweak baryogenesis.

We investigate the origin and evolution of primordial electric and magnetic fields in the early universe, when the expansion is governed by a cosmological constant Λ0. Using the gravitoelectromagnetic inflationary formalism with A0 = 0, we obtain the power of spectrums for large-scale magnetic fields and the inflaton field fluctuations during inflation. A very important fact is that our formalism is naturally non-conformally invariant.