False Vacuum State Research Articles

Gravitational radiation from colliding vacuum bubbles.

In the linearized-gravity approximation we numerically compute the amount of gravitational radiation produced by the collision of two true-vacuum bubbles in Minkowski space. The bubbles are separated by distance d and we calculate the amount of gravitational radiation that is produced in a time \ensuremath{\tau}\ensuremath{\sim}d (in a cosmological phase transition \ensuremath{\tau} corresponds to the duration of the transition, which is expected to be of the order of the mean bubble separation d). Our approximations are generally valid for \ensuremath{\tau}\ensuremath{\lesssim}${\mathit{H}}^{\mathrm{\ensuremath{-}}1}$. We find that the amount of gravitational radiation produced depends only upon the grossest features of the collision: the time \ensuremath{\tau} and the energy density associated with the false-vacuum state, ${\mathrm{\ensuremath{\rho}}}_{\mathrm{vac}}$. In particular, the spectrum ${\mathit{dE}}_{\mathrm{GW}}$/d\ensuremath{\omega}\ensuremath{\propto}${\mathrm{\ensuremath{\rho}}}_{\mathrm{vac}}^{2}$${\mathrm{\ensuremath{\tau}}}^{6}$ and peaks at a characteristic frequency ${\mathrm{\ensuremath{\omega}}}_{\mathrm{max}}$\ensuremath{\simeq}3.8/\ensuremath{\tau}, and the fraction of the vacuum energy released into gravitational waves is about 1.3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$(\ensuremath{\tau}/${\mathit{H}}^{\mathrm{\ensuremath{-}}1}$${)}^{2}$, where ${\mathit{H}}^{2}$=8\ensuremath{\pi}G${\mathrm{\ensuremath{\rho}}}_{\mathrm{vac}}$/3 (\ensuremath{\tau}/${\mathit{H}}^{\mathrm{\ensuremath{-}}1}$ is expected to be of the order of a few percent). We address in some detail the important symmetry issues in the problem, and how the familiar ``quadrupole approximation'' breaks down in a most unusual way: it overestimates the amount of gravitational radiation produced in this highly relativistic situation by more than a factor of 50. Most of our results are for collisions of bubbles of equal size, though we briefly consider the collision of vacuum bubbles of unequal size. Our work implies that the vacuum-bubble collisions associated with strongly first-order phase transition are a very potent cosmological source of gravitational radiation.

Aspects of reheating in first-order inflation

We study reheating in theories where inflation is completed by a first-order phase transition. In these scenarios, the Universe decays from its false vacuum state by bubble nucleation. We follow the Universe through the phase transition beginning with bubble nucleation and ending with particle production from wall collisions. In the first stage of reheating, vacuum energy is converted into kinetic energy for the bubble walls. To help understand this phase we derive a simple expression for the equation of state of a universe filled with expanding bubbles. Eventually the bubble walls collide. The production of particles during wall collisions from both classical and quantum processes is examined. We study classical scalar wave production through numerical simulations of two-bubble collisions, clarifying and extending previous work by Hawking, Moss and Stewart. We go on to discuss direct quantum particle production due to couplings between the inflaton and other fields. We calculate particle production for colliding walls in both sine-Gordon and φ 4 theories. Our results indicate that both classical and quantum processes are quite efficient for models with double-well potentials, but can be suppressed for models with potentials that are periodic. In addition, we show that particles with masses well above the mass of the inflaton can be produced if the walls are highly relativistic. The relevance of our work for recently proposed models of first-order inflation is discussed.

The early Weyl universe

The consequences of a period of Weyl invariance in the early universe are investigated. It is argued that the natural outcome of such a period is a Kaluza-Klein style compactification of an internal space in which any time variation of the scale factor of this space is absorbed (via a Weyl transformation) into the gravitational coupling. A five-dimensional test model is shown to undergo exponential inflation of the space-time sector due to a false vacuum state of the non-metric part of the connection.

Can a man-made Universe be created by quantum tunneling without an initial singularity?

Essentially all modern particle theories suggest the possible existence of a false vacuum state – a metastable state with an energy density that cannot be lowered except by means of a very slow phase transition. Inflationary cosmology makes use of such a state to drive the expansion of the big bang, allowing the entire observed universe to evolve from a very small initial mass. A sphere of false vacuum in our present universe, if larger than a certain critical mass, could inflate to form a new universe which would rapidly detach from its parent. A false vacuum bubble of this size, however, cannot be produced classsically unless an initial singularity is present from the outset. We therefore explore the possibility that a bubble of subcritical size, which classically would evolve to a maximum size and collapse, might instead tunnel through a barrier to produce a new universe. We estimate the tunneling rate using semiclassical quantum gravity, and discover some interesting ambiguities in the formalism.

Gravitational nucleation of vacuum phase transitions by compact objects.

The possibility of gravitationally condensed material objects (such as neutron stars, monopoles, etc.) acting as nucleation sites for the decay of the false vacuum is examined. The Einstein equations are solved to determine the classical motion of thin-wall bubbles of the true vacuum which form in or around spherically symmetric bodies of uniform-density perfect fluid. Certain decays of negative-energy-density false-vacuum states, which were previously considered to be forbidden, are shown to be locally possible in the neighborhood of a star. In these solutions, bubbles of the true vacuum form inside the star and then oscillate between two radii. The Euclidean action for bubbles which form at R=3M around a uniform-density star is calculated and compared to the action for O(4)-symmetric decay and for decay nucleated by a black hole. The action in the presence of a star is found to be significantly smaller than the other cases. It thus appears that gravitationally condensed material objects in the appropriate mass and radius range can act as nucleation centers for bubbles of the true vacuum, greatly hastening the phase transition and making supercooling difficult or even impossible to achieve.

Dynamics of false-vacuum bubbles.

The possibility of localized inflation is investigated by calculating the dynamics of a spherically symmetric region of false vacuum which is separated by a domain wall from an infinite region of true vacuum. For a range of initial conditions, the false-vacuum region will undergo inflation. An observer in the exterior true-vacuum region will describe the system as a black hole, while an observer in the interior will describe a closed universe which completely disconnects from the original spacetime. We suggest that this mechanism is likely to lead to an instability of Minkowski space: a region of space might undergo a quantum fluctuation into the false-vacuum state, evolving into an isolated closed universe; the black hole which remains in the original space would disappear by quantum evaporation. The formation of these isolated closed universes may also be relevant to the question of information loss in black-hole formation.

Can black holes nucleate vacuum phase transitions?

The decay of false-vacuum states through a first-order phase transition in the presence of a Schwarzschild black hole is studied in the zero-temperature limit. The equations of motion for a thin-wall bubble which forms in a spherically symmetric fashion around a Schwarzschild--de Sitter (or --anti--de Sitter) black hole are derived. The Euclidean action for these bubble solutions is calculated and is found to be smaller, by up to a factor of roughly 2, than the O(4)-symmetric action in which no black hole is present. It thus appears that a black hole can act as an effective nucleation center for a first-order vacuum phase transition. It will then be more difficult (require more ``fine-tuning'' of the potential) than was previously believed to achieve supercooling of a false-vacuum state, provided that appropriate-mass black holes are present.