Everything about False Vacuum totally explained
In
quantum field theory, a
false vacuum is a
metastable sector of
space which appears to be a
perturbative vacuum but is unstable to
instanton effects which may
tunnel to a lower energy state. This tunneling can be caused by quantum fluctuations or the creation of high energy particles. Simply put, the false vacuum is a
local minimum, but not the lowest energy state, even though it may remain stable for some time. This is analogous to metastability for
first order phase transitions.
Bubble nucleation
In a physical theory in a false vacuum, the system moves to a lower energy state – either the true vacuum, or another, lower energy vacuum – through a process known as bubble
nucleation. In this, instanton effects cause a bubble to appear in which fields have their true vacuum values inside. Therefore, the interior of the bubble has a lower energy. The walls of the bubble (aka
domain walls) have a
surface tension, as energy is expended as the fields roll over the potential barrier to the lower energy vacuum. The most likely size of the bubble is determined in the
semiclassical approximation to be such that the bubble has zero total change in the energy: the decrease in energy by the true vacuum in the interior is compensated by the tension of the walls.
Expansion of bubble
Any
increase in size of the bubble will
decrease its potential energy, as the energy of the wall increases as the area of a sphere
but the negative contribution of the interior increases more quickly, as the volume of a sphere
. Therefore, after the bubble is nucleated, it quickly begins expanding at very nearly the speed of light. The excess energy contributes to the very large kinetic energy of the walls. If two bubbles are nucleated and they eventually collide, it's thought that particle production occurs where the walls collide.
The tunneling rate is increased by increasing the energy difference between the two vacua and decreased by increasing the height or width of the barrier.
Gravitational effects
The addition of
gravity to the story leads to a considerably richer variety of phenomena. The key insight is that a false vacuum with positive potential energy density is a
de Sitter vacuum, in which the potential energy acts as a
cosmological constant and the
Universe is undergoing the exponential expansion of
de Sitter space. This leads to a number of interesting effects, first studied by
Coleman and de Luccia:
Space with zero potential energy
Tunnelling from a space with zero potential energy (
for example Minkowski space) to negative potential energy leads to the following. The walls of the bubble grow at the speed of light, as described above. However, the interior of the bubble rapidly collapses, as
anti-de Sitter space and the universe ends (see
ultimate fate of the universe and
vacuum metastability event, below).
Space with positive potential energy
Tunneling from a space of positive potential energy (
de Sitter space) to one of vanishing potential energy (Minkowski space) leads to the following. The volume of the bubble continues to grow at the speed of light. However, since the exterior of the bubble is expanding exponentially while the Minkowski space is not—unlike the non-gravitational case—the whole of space time need never be dominated by the lower energy vacuum. If the tunnelling rate is slow enough, the exponentially expanding space in the false vacuum state can expand sufficiently quickly so that the bubbles of lower-energy space never begin to collide and convert all of space-time to the lower energy state. That is, the tunnelling is competing with rapid expansion, and the exponential expansion can be so rapid that the tunneling effect is overwhelmed.
From positive potential energy to lower, positive potential energy
Tunnelling from positive potential energy to lower, positive potential energy leads to the following. Just as for the above case, the more rapid exponential expansion of the higher energy false vacuum can continue to dominate.
From positive potential energy to negative potential energy
Tunneling from positive potential energy to negative potential energy leads to the following. This effect is highly suppressed: the expansion of the positive energy vacuum dominates the contraction of the negative energy vacuum.
A final kind of tunnelling
A final kind of tunnelling is the
Hawking-Moss instanton. This occurs when the size of the Coleman–de Luccia bubble is larger than the size of the universe, in a
closed universe, or of the horizon. In this case, the entire universe tunnels from the false vacuum to the true vacuum at once.
Developments of theory
Alan Guth in his original proposal for
cosmic inflation proposed that inflation could end through quantum mechanical bubble nucleation of the sort described
above. See
History of Chaotic inflation theory. It was soon understood that a homogeneous and isotropic universe couldn't be preserved through the violent tunneling process. This led
Andrei Linde and, independently,
Andreas Albrecht and
Paul Steinhardt to propose "new inflation" or "slow roll inflation" in which no tunnelling occurs, and the inflationary scalar field instead rolls down a gentle slope.
String landscape
A more recent application of these tunnelling phenomena in cosmology and particle physics is the
string landscape in which string theory is conjectured to be populated by an exponentially large "discretuum" of false vacua, and the small observed value of the cosmological constant (see
dark energy) can be explained by the
anthropic principle and quantum mechanical tunnelling to the lowest positive energy vacuum.
Vacuum metastability event
In their paper, Coleman and de Luccia noted:
» The possibility that we're living in a false vacuum has never been a cheering one to contemplate. Vacuum decay is the ultimate ecological catastrophe; in the new vacuum there are new constants of nature; after vacuum decay, not only is life as we know it impossible, so is chemistry as we know it. However, one could always draw stoic comfort from the possibility that perhaps in the course of time the new vacuum would sustain, if not life as we know it, at least some structures capable of knowing joy. This possibility has now been eliminated., and in
2000 by
Stephen Baxter.
Many-worlds interpretation of quantum mechanics
According to the
many-worlds interpretation of
quantum mechanics, the universe won't end this way. Instead, each time a quantum event happens that causes the universe to decay from a false vacuum to a true
vacuum state, the universe splits into several new worlds. In some of the new worlds the universe decays; in some others the universe continues as before.
Particle accelerator
One scenario is that, rather than quantum tunnelling, a
Particle accelerator, which produces very high
energies in a very small area, could create sufficiently high energy density as to penetrate the barrier and stimulate the decay of the false vacuum to the lower energy vacuum. Hut and Rees, however, have determined that because we've observed
cosmic ray collisions at much higher energies than those produced in terrestrial particle accelerators, that these experiments will not, at least for the foreseeable future, pose a threat to our vacuum. Particle accelerations have reached energies of only approximately four thousand billion
electron volts (4 ×10
3 GeV). Cosmic ray collisions have been observed at and beyond energies of 10
11 GeV, the so-called
Greisen-Zatsepin-Kuzmin limit. John Leslie has argued that if present trends continue, particle accelerators will exceed the energy given off in cosmic ray collisions by the year 2150.
This event would be contingent on our living in a metastable vacuum, an issue which is far from resolved. Worries about the vacuum metastability event are reminiscent of the controversy about turning the
Relativistic Heavy Ion Collider on.
Further Information
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