Four Questions on vacuum phase transitions in the Universe...

[Suekdccia]

TL;DR Summary

4 Questions on vacuum phase transitions in the universe...?

I am interested in the topic of vacuum phase transitions in models of the universe. One popular instance of this is a vacuum decay from a metastable vacuum energy level to a "true" one (in which the vacuum would sit at the lowest possible energy level depending on the model)


I have 4 questions on this topic, although it's okay if I get an answer that does not cover all of them necessarily:


1. I have read that there can be both down-tunneling and up-tunneling events (although the up-tunneling events are very suppressed) there are terminal vacua (like AdS or Minskowski spaces) that cannot up-tunnel to any vacua (https://digital.csic.es/bitstream/10261/87436/1/Schellekens.pdf ; page 47). However, if two vacuum bubble events collide, the resultant energy could trigger an up-tunneling of the vacuum, and this could happen between two bubbles of terminal vacua (https://arxiv.org/pdf/1005.3506). However, the new vacuum could not have a higher energy level than the parent vacuum; but if the terminal vacuum bubbles that collided had a zero energy level, then how can there be an up-tunneling to a higher energy level?


2. Can black holes trigger a vacuum phase transition? Can they have enough Hawking temperature to trigger a thermal phase transition? Or perhaps a slow phase transition (https://arxiv.org/pdf/2310.06901 ; https://inspirehep.net/literature/249056)?


3. A vacuum phase transition catalized by particle collisions is rather suppressed as this shows (https://arxiv.org/abs/2301.03620). However does this apply only at the present state of the universe? I mean, will it be also suppressed in the far future once the universe is approaching heat death and almost all what is left are quantum fluctuations? (I did a similar question some days ago, but I would like to focus it on the far future instead of the present universe)


4. Does the energy content of the universe have any influence in vacuum phase transitions? I mean, if there's enough energy/mass content in the universe, could it up-tunnel to a higher vacuum energy level (compared to a universe with almost no energy/mass content)? Perhaps if there is enough energy/mass content in the universe some kind of quantum fluctuation could cause the vacuum to be in a higher energy level (transforming it into a metastable one)? Or this is nonsense and the energy content of the universe is completely unrelated to vacuum phase transitions?

 

[Mordred]

I believe part of your issue with the question above seems to stem from some confusion on what is meant by the term vacuum expectation value.

The VeV is not the energy density nor the total energy density. It is an expectation value which involves correlation functions (Greens functions).
Secondly the term vacuum bubble specifically relate to Feymann path integrals. You can further have a probability number density


Both the above will vary on how they are applied depending on the initial and final states being describes. For example the Higgs field is a gauge symmetry breaking scenario where the VeV directly related to the Fermi constant.

So really your going about understanding vacuum, VeV etc the wrong way. How QFT describes a vacuum bubble isn't necessarily the same as describing say the vacuum state described by DE in Cosmology. In cosmology the vacuum term is described by the relationship behind the kinetic and potential energy terms described by the scalar field equation of state..
This is not the case with the vacuum described by QFT related processes such as the Higgs field.

 

[Suekdccia]

In cosmology the vacuum term is described by the relationship behind the kinetic and potential energy terms described by the scalar field equation of state..

I think this is the way I was thinking about it as I read that different vacua have different energy levels (without getting into details of the math)

So are the way QFT describes the vacuum completely unrelated to the way cosmology does then? Can my questions be answered? Or they do not make sense?

 

[Mordred]

Let's put it this way question one can only be answered in the context given by the vacuums described by the article which uses the Cosmology way (scalar field equations of state also used by eternal inflation) the vacuum bubbles here are De-Sitter spacetimes with which the positive De-Sitter spacetime the potential energy term exceeds the kinetic energy term.
The anti De-Sitter spacetime the reverse is true.

We don't involve the VeV in this scenario it's rather meaningless to do so nor can you answer how Hawking radiation would interact with either spacetime without a particle composition of those spacetimes and an identity of the particle used for Hawking radiation.
The De-Sitter spacetimes are using instantons which is much like a placeholder at best a quasi particle. Hawking radiation typically uses virtual gauge bosons such as a photon so how that interacts with instantons isn't answerable.
Not without Speculations beyond the scope of the forum rules.

As far as your last question goes my answer is the same in your other related thread in that I can see no possibility for up tunnelling from a low energy density universe to a higher density universe even under Chaotic eternal universe descriptive for Bubble universe due to runaway inflation. (The likely hood is described by article 2) where they provide the constraints but those constraints are determined via mathematics and doesn't address a scenario where it could be possible in the real universe outside of the mathematics.

 

[Suekdccia]

Let's put it this way question one can only be answered in the context given by the vacuums described by the article which uses the Cosmology way (scalar field equations of state also used by eternal inflation) the vacuum bubbles here are De-Sitter spacetimes with which the positive De-Sitter spacetime the potential energy term exceeds the kinetic energy term.
The anti De-Sitter spacetime the reverse is true.

We don't involve the VeV in this scenario it's rather meaningless to do so nor can you answer how Hawking radiation would interact with either spacetime without a particle composition of those spacetimes and an identity of the particle used for Hawking radiation.
The De-Sitter spacetimes are using instantons which is much like a placeholder at best a quasi particle. Hawking radiation typically uses virtual gauge bosons such as a photon so how that interacts with instantons isn't answerable.
Not without Speculations beyond the scope of the forum rules.

As far as your last question goes my answer is the same in your other related thread in that I can see no possibility for up tunnelling from a low energy density universe to a higher density universe even under Chaotic eternal universe descriptive for Bubble universe due to runaway inflation. (The likely hood is described by article 2) where they provide the constraints but those constraints are determined via mathematics and doesn't address a scenario where it could be possible in the real universe outside of the mathematics.

Mmmh...I still have some confusion regarding the first question because the article says that two percolating vacuum bubbles with zero energy density can collide so that the resultant energy could trigger an up-tunneling of the vacuum. But at the same time, the authors say that this new vacuum could not have a higher energy density than the "parent" vacua. But if the parent vacua had a 0 energy density, then the resulting vacuum would not up-tunnel. So isn't this a contradiction?

Also, as for my last question, just to clarify, you say that the #2 article gives some mathematical way of up-tunneling a low energy density vacuum into a high-energy density one, it does not give a specific mechanism in which it could be done?


Also, again, regarding the last question, taking the "cosmological" definition of the vacuum energy (with the potential and kinetic terms in the state equation) wouldn't the energy content of the universe be related to the possibility of an up-tunneling? I mean, essentially my question would be, is it possible that the mass/energy content of a given universe could be "transferred" to the vacuum (if that even makes sense) so that we get a vacuum with a higher energy content (although we may not know exactly how can it be done)? Or aty least, could the mass/energy content of the universe have any influence on vacuum phase transitions?

 

[Mordred]

As to the first part the distinction is the terminal vacuum where the kinetic energy term exceeds the potential energy term. This gives you the negative energy state described this is the same manner negative vacuum is described via the equations of state for w=-1 Now potentially you can have another bubble where the potential energy term exceeds the kinetic term for a positive vacuum. So lets set this for w=+1

Now set first one to A second to B. Resultant C
Vacuum A could have lower density than B but when it collides with B the higher potential energy due to the gravitational field could theoretically draw on the inflatons from A as gravity is attractive only. The repulsive gravity is the negative vacuum scenario it's a poor misleading descriptive when its really more accurate to treat it as a pressure term.
Hope that helps

As to phase transitions those occur when you have symmetry breaking of particle properties so in order to get another phase transition this would result in previously unknown particles or unknown particle properties of existing particles...
Let's use a known scenario electroweak symmetry breaking. Prior to electrowesk symmetry breaking particles are in thermal equilibrium and symmetric. When the universe cooled down various particle species drops out of thermal equilibrium and acquire mass via the Higgs field. (This is a phase transition)

So the only way to answer the second part with a yes is if there are particles or particle generation that has not been predicted nor detected.

Edit: also keep in mind that I am not too familiar with ADS/CFT beyond the general understanding behind that theory. Which relates to the second paper including the Penrose diagram. This relates to the different observers as different observers can measure energy and energy density differently (good source Unruh effect) which also relates to Hawking radiation in terms of cosmological horizons.
Also zero energy may or may not be truly zero you can arbitrarily set any value as zero which is often done with vacuum solutions or another common field treatment such as lattice networks.

You can set the baseline as zero even though it has a non zero energy level

 

[Suekdccia]

As to phase transitions those occur when you have symmetry breaking of particle properties so in order to get another phase transition this would result in previously unknown particles or unknown particle properties of existing particles...
Let's use a known scenario electroweak symmetry breaking. Prior to electrowesk symmetry breaking particles are in thermal equilibrium and symmetric. When the universe cooled down various particle species drops out of thermal equilibrium and acquire mass via the Higgs field. (This is a phase transition)

So the only way to answer the second part with a yes is if there are particles or particle generation that has not been predicted nor detected.

From this I'm getting that vacuum phase transitions are not the same as a vacuum up-tunneling or down-tunneling to higher/lower energy vacua, correct?

 

[Mordred]

Correct now your getting it with Phase transition vacuum and vacuum bubbles is defined differently as your now applying QM/QFT in which a vacuum bubble involves the Feymann integrals