# False vacuum

A scalar field φ in a false vacuum. Note that the energy E is higher in the false vacuum than that in the true vacuum or ground state, but there is a barrier preventing the field from classically rolling down to the true vacuum. Therefore, the transition to the true vacuum must be stimulated by the creation of high-energy particles or through quantum-mechanical tunneling.

In quantum field theory, a false vacuum is a hypothetical vacuum that is somewhat, but not entirely, stable. It may last for a very long time in that state, and might eventually move to a more stable state. The most common suggestion of how such a change might happen is called bubble nucleation – if a small region of the universe by chance reached a more stable vacuum, this "bubble" (also called "bounce"[1][2]) would spread.

A false vacuum exists at a local minimum of energy and is therefore not stable, in contrast to a true vacuum, which exists at a global minimum and is stable. It may be very long-lived, or metastable.

## Definition of true vs false vacuum

A vacuum is defined as a space with as little energy in it as possible. Despite the name, the vacuum still has quantum fields. A true vacuum is a global minimum of energy, and is commonly assumed to coincide with a physical vacuum state we live in.

Synonyms for physical vacuum state are the following: Standard Model vacuum, normal vacuum, normal space, physical space, our space-time, fabric of space-time, universe.

The configuration with quantum fields at global energy minimum is stable. The false vacuum is a local minimum, but not the lowest energy state of quantum fields.

It is possible that a physical vacuum state is a configuration of quantum fields representing a local minimum but not global minimum of energy. In this case vacuum state is called a "false vacuum".

## Implications

### Existential threat

If a more stable vacuum state were able to arise, the effects may vary from complete cessation of existing fundamental forces, elementary particles and structures comprising them, to subtle change in some cosmological parameters, mostly depending on potential difference between true and false vacuum. Some false vacuum decay scenarios are compatible with survival of structures like galaxies and stars[3][4] or even life[5] while others involve the full destruction of baryonic matter[6] or even immediate gravitational collapse of the universe,[7]^Note 1 although in this last case the possibility to causally connect (i.e nucleate) the true vacuum from inside of the false vacuum area is dubious.[8]

In a 2005 paper published in Nature, as part of their investigation into global catastrophic risks, MIT physicist Max Tegmark and Oxford philosopher Nick Bostrom calculate the natural risks of the destruction of the Earth at less than 1 per gigayear from all events, including a transition to a lower vacuum state. They argue that due to observer selection effects, we might underestimate the chances of being destroyed by vacuum decay because any information about this event would reach us only at the instant when we too were destroyed. This is in contrast to events like risks from impacts, gamma-ray bursts, supernovae and hypernovae, the frequencies of which we have adequate direct measures.[9]

### Inflation

• The inflation itself may be the consequence of the Higgs field trapped in a false vacuum state[10] with Higgs self-coupling λ and its βλ function very close to zero at the Planck scale.[11]:218 A future electron-positron collider would be able to provide the precise measurements of the top quark needed for such calculations.[11]
• Chaotic Inflation Theory suggests that the universe may be in either a false vacuum or a true vacuum state.
• Alan Guth, in his original proposal for cosmic inflation,[12] 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 could not be preserved through the violent tunneling process. This led Andrei Linde[13] and, independently, Andreas Albrecht and Paul Steinhardt,[14] to propose "new inflation" or "slow roll inflation" in which no tunnelling occurs, and the inflationary scalar field instead graphs as a gentle slope.

## Vacuum decay varieties

### Electroweak vacuum decay

Electroweak vacuum stability landscape as estimated in 2012[11]

Electroweak vacuum stability landscape as estimated in 2018[2]

The stability criteria for Electroweak interaction was first formulated in 1979,[15] that time as function of masses of theoretical Higgs boson and heaviest fermion. Discovery of Top quark in 1995 and Higgs boson in 2012 have allowed to validate the criteria against experiment, therefore since 2012 Electroweak interaction is considered as most promising candidate for metastable fundamental force.[11]. The corresponding false vacuum hypothesis is called either 'Electroweak vacuum instability' or 'Higgs vacuum instability'.[16]. The present false vacuum state is called ${\displaystyle dS}$  (De Sitter space), while tentative true vacuum is called ${\displaystyle AdS}$  (Anti-de Sitter space).[17][18]

Diagrams on right are showing the uncertainty ranges of Higgs boson and top quark masses as oval-shaped lines. Underlying colors are indicating if the electroweak vacuum state is likely to be stable, merely long-lived or completely unstable for given combination of masses.[19][20] The "electroweak vacuum decay" hypothesis was sometimes misreported as the Higgs boson "ending" the universe.[21][22][23] A 125.18±0.16 GeV/c2[24] Higgs boson mass is likely to be on the metastable side of stable-metastable boundary (estimated in 2012 as 123.8–135.0 GeV. [11] ) However, a definitive answer requires much more precise measurements of the top quark's pole mass,[11], although improved measurement precision of Higgs boson and top quark masses further reinforced the claim of physical electroweak vacuum being in the metastable state as in 2018.[2] Nonetheless, new physics beyond the Standard Model of Particle Physics could drastically change the stability landscape division lines, rendering previous stability and metastability criteria incorrect. [25][26]

If measurements of Higgs boson and top quark suggests that our universe lies within a false vacuum of this kind, then it would imply—more than likely in many billions of years[27] the bubble's effects would be expected to propagate across the universe at nearly the speed of light from wherever it occurred. However space is vast—with even the nearest galaxy being over 2 million light-years from us, and others being many billions of light-years distant, so the effect of such an event would be unlikely to arise here for billions of years after first occurring.[28][27]

## True vacuum bubble nucleation

In the theoretical physics of the 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.[29][30][31][32][33][1] 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 (or domain walls) have a surface tension, as energy is expended as the fields roll over the potential barrier to the lower energy vacuum. The critical size of the bubble is determined in the semi-classical 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.

To convert initially small true vacuum bubble (bounce) into bubble with zero total energy, an energy barrier must be overcome, and barrier height ${\displaystyle \Phi _{c}}$  is follows equation[1]

${\displaystyle \Phi _{c}=3A/4R^{2}-\Delta \Phi ;}$

(Eq. 1)

, where ${\displaystyle \Delta \Phi }$  - potential difference between true and false vacuums, ${\displaystyle A}$  is unknown constant (surface tension of interface between different vacua), and ${\displaystyle R}$  - radius of bubble. Perhaps the unknown constant ${\displaystyle A}$  is so high that bubble large enough to have barrier vanished has never yet been formed anywhere in the universe. Rewriting the Eq. 1, one can get true vacuum bubble critical radius as

${\displaystyle R={\sqrt {3A/(4\Delta \Phi )}};}$

(Eq. 2)

Bubble of true vacuum smaller than critical size can overcome the potential barrier due to the quantum tunnelling of instantons to lower energy states. Tunneling can be caused by quantum fluctuations, and tunneling rate to expanding state for bubble smaller than critical size can be expressed as[34]

${\displaystyle \omega ={\tfrac {1}{A}}{\sqrt {\tfrac {2\Phi _{c}}{h}}}e^{-\Phi _{c}/h};}$

(Eq. 3)

where ${\displaystyle h}$  is Planck constant.

Also, small bubble of true vacuum can be inflated to critical size by externally supplied energy,[35] although required energy densities are several orders of magnitude beyond capability of any natural or artificial process.[6] Energy-driven bubble inflation mechanism should not be confused with the speculative nucleation barrier lowering by gravity field of miniature black holes.

### False vacuum decay nucleation seeds

• In a study in 2015,[36] it was pointed out that the vacuum decay rate could be vastly increased in the vicinity of black holes, which would serve as a nucleation seed.[37] According to this study a potentially catastrophic vacuum decay could be triggered at any time by primordial black holes, should they exist. The subsequent study in 2017 has indicated that the nucleated true vacuum bubble would collapse into a primordial black hole rather than originate from it.[38] In 2019, it was found that although small non-spinning black holes may increase true vacuum nucleation rate, rapidly spinning black holes will stabilize false vacuum to decay rates lower than expected for flat space-time.[39]
• If particle collisions produce mini black holes then energetic collisions such as the ones produced in the Large Hadron Collider (LHC) could trigger such a vacuum decay event. This scenario is most publicized yet most unrealistic, because if such mini black holes can be created in collisions, they would also be created in the much more energetic collisions of cosmic radiation particles with planetary surfaces or during early epoch as tentative primordial black holes.[40] Hut and Rees[41] note that, because we have observed cosmic ray collisions at much higher energies than those produced in terrestrial particle accelerators, these experiments should not, at least for the foreseeable future, pose a threat to our current vacuum. Particle accelerators have reached energies of only approximately eight tera electron volts (8×1012 eV). Cosmic ray collisions have been observed at and beyond energies of 5*1019 eV, six million times more powerful – the so-called Greisen–Zatsepin–Kuzmin limit – and cosmic rays in vicinity of origin may be more powerful yet. Against this, John Leslie has argued[42] that if present trends continue, particle accelerators will exceed the energy given off in naturally occurring cosmic ray collisions by the year 2150. Fears of this kind were raised by critics of both the Relativistic Heavy Ion Collider and the Large Hadron Collider at the time of their respective proposal, and determined to be unfounded by scientific inquiry.
• In a study in 2020, it was proposed that cosmic string may also serve as nucleation site for the false vacuum decay.[43]
• Nucleation energy barrier can be overcome by extreme energy density associated with magnetic monopole.[6]

### Expansion of bubble

As soon as a bubble of lower-energy vacuum grows beyond the critical radius defined by Eq. 2, the bubble's wall will begin to accelerate outward. The expansion will then decrease the bubble`s potential energy, as the energy of the wall increases as the surface area of a sphere ${\displaystyle 4\pi r^{2}}$  but the negative contribution of the interior increases more quickly, as the volume of a sphere ${\displaystyle \textstyle {\frac {4}{3}}\pi r^{3}}$ . With the expected large potential differences between false and true vacuum states in most vacuum decay scenarios, the velocity of the bubble surface becomes practically indistinguishable from the speed of light in a fraction of second. The single bubble does not produce any gravitational effects on surrounding objects during expansion, because the negative energy density of the bubble interior is cancelled by the positive kinetic energy of the wall.[7] If two bubbles are nucleated and they eventually collide, it is thought that particle production would occur where the walls collide.

## False vacuum decay in fiction

False vacuum decay event is occasionally used as a plot device in works picturing a doomsday event.

## Notes

^Note 1 A paper by Coleman and de Luccia which attempted to include simple gravitational assumptions into these theories noted that if this was an accurate representation of nature, then the resulting universe "inside the bubble" in such a case would appear to be extremely unstable and would almost immediately collapse:

In general, gravitation makes the probability of vacuum decay smaller; in the extreme case of very small energy-density difference, it can even stabilize the false vacuum, preventing vacuum decay altogether. We believe we understand this. For the vacuum to decay, it must be possible to build a bubble of total energy zero. In the absence of gravitation, this is no problem, no matter how small the energy-density difference; all one has to do is make the bubble big enough, and the volume/surface ratio will do the job. In the presence of gravitation, though, the negative energy density of the true vacuum distorts geometry within the bubble with the result that, for a small enough energy density, there is no bubble with a big enough volume/surface ratio. Within the bubble, the effects of gravitation are more dramatic. The geometry of space-time within the bubble is that of anti-de Sitter space, a space much like conventional de Sitter space except that its group of symmetries is O(3, 2) rather than O(4, 1). Although this space-time is free of singularities, it is unstable under small perturbations, and inevitably suffers gravitational collapse of the same sort as the end state of a contracting Friedmann universe. The time required for the collapse of the interior universe is on the order of ... microseconds or less.

The possibility that we are 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.

The second special case is decay into a space of vanishing cosmological constant, the case that applies if we are now living in the debris of a false vacuum which decayed at some early cosmic epoch. This case presents us with less interesting physics and with fewer occasions for rhetorical excess than the preceding one. It is now the interior of the bubble that is ordinary Minkowski space ...

— Sidney Coleman and Frank De Luccia

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