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

 

[Suekdccia]

Correct now your getting it.

Alright, thanks! Then I was mixing terminology, I apologize (I'm not a physicist after all )

Okay, so let me give a bit more of context on my last two questions (#3 and #4) which essentially were "inspired" after watching a video by Leonard Susskind on entropy, the future of the universe and the Poincaré recurrence theorem

From minute (34:00) towards the end, he tells the audience how we could escape from the problem of recurrences (which usually lead to Boltzmann brains) in a universe with a cosmological constant (which would have a radiating cosmological horizon, leading to recurrence problems). He says that if the universe has a cosmological constant, it means that the vacuum has a non-zero energy level, so if it was in a metastable state it could eventually decay (via quantum fluctuations in the far future for example) into a true vacuum level with essentially zero vacuum energy (or no cosmological constant i.e. no "dark energy"). Then once this happens, the cosmological horizon disappears and no more recurrences do occur (and we do not end up concluding that we are Boltzmann brains).

However, I was wondering if this would be maintained forever, or whether it could be the case that the vacuum might end up again with a cosmological constant (which I suppose that to get to this situation it would have to up-tunnel back into a metastable vacuum state, or a vacuum with a non-zero energy level). Of course, if we have no energy, then the vacuum could not magically up-tunnel into anything, as it would violate the principle of energy conservation.

But what about if the universe had enough mass/energy content? I mean, even if the vacuum energy was set at zero and it would not have a cosmological constant, consider a universe with enough mass and "regular" energy content of any type: thermal, electrical, potential, kinetic... Could it be possible that this energy could cause an up-tunneling?

Then goes the other question: If this up-tunneling is highly suppressed (as the article from question #3 suggests) and very unlikely to occur in nature (though cosmic rays collisions for instance), would the far-future universe conditions (approaching heat death) also suppress this? Or this only applies to the present universe? I ask this because when physicists talk about a possible future vacuum decay event, they mention the possibility that it could be caused by a quantum fluctuation. But if quantum fluctuations would not be suppressed in doing so in the future, would it be similar to a future up-tunneling of the vacuum caused by a future collision event of cosmic rays?

 

[Mordred]

I take it from the last post and subsequent posts your primary interest is mainly future fate of the universe as opposed to quantum processes involved in VeV and phase transitions if that's correct then it's advisable to request a moderator to move this thread to Cosmology as the primary discussion revolves in the Cosmology based treatment via the FLRW metric equations of state.

I will look over your last post after work then get back to you on your last post.

 

[Mordred]

Here is thing with Boltzmann brains and Poincare recurrence it is a highly Specualtive theory that relies heavily on the detail that there is a statistical possibility of occurance. However given the timeliness involved that are a great many orders of magnitude beyond the age of the Universe that likelyhood is incredibly low.
Those probabilities that rely on the Cosmological constant involve whether or not w-1 is the correct equation of state. This value describes a non evolving (constant) parameter.
In regards to Higgs field and phase transitions which is also involved in Boltzmann Brain papers it suggests the Higgs field may or may be in a true vacuum state thus leading to new physics and potentially new symmetry break.
Once again based on an extremely low likelyhood but still possible.

However that being said that's about the extent I've ever looked into Boltzmann Brains and Poincare recurrence. Which quite frankly your likely more familiar with the papers involving that Specualtive theory I am.

That being said understanding the physics behind the arguments is something I can help with. One challenge you will have if you wish pursue this and gain a better understanding is that in order to understand the thermodynamics and the probability functions involving thermodynamics (including entropy) will require a good understanding of Statistical mechanics.
QFT obviously for field treatments involving the SM of particles and the FLRW metric which is a GR solution.
Judging from your question involving mass and energy terms consider the following statements. (You may already them but it's best to make sure)

Energy us a property of an object, system , state or field that describes the ability to perform work. Mass being the property describing the resistance to inertia change or acceleration for short of any of the above.
These are not quantities that exists on its own.

Now knowing how to properly think of energy and mass consider the following. Let's take an ensemble of particles and represent them by a field. Keep in mind a field is any collection of objects, values or other mathematical object that does not necessarily relate to a physical (measurable ) value. You can have a strictly probability field for example.

In QM the Heienburg uncertainty principle describes zero point energy when you apply this to your ensemble of particles under field treatment. In this case we can use momentum space. If you apply the harmonic oscillator to every coordinate you will end up with infinite energy prior to renormalization.
QFT renormalizes the harmonic oscillator naturally but you still have a non zero energy content. However we can only measure the potential difference between two field coordinates much like by analogy you cannot measure voltage by placing the leads of your multimeter at two ends of wire with no resistance or load. We'll resistance is described by our mass term voltage describing the potential difference.

Hence we can readily set our baseline (zero point) as the most uniform stable point of the harmonic oscillator which although has non zero energy is set as zero)

That should help you answer your own question regarding how a ground state when you introduce some further quantum fluctuation to your systems/states described by those papers can lead to higher energy states particularly if a small fluctuation expands throughout the system and potentially lead to further fluctuations.
The above can also give rise to particle creation/annihilation events. For example the number density of any particle species can be estimated by the blackbody temperature of the CMB via the Einstein Boltzmann statistics for bosons and the Fermi-Statistics for fermions.

That should help answer how a ground state under a field treatment that employs the momentum terms (mass, energy) can alter from the ground state to a different energy value. The requirement being potential field differences between any two or more reference points

 

[Suekdccia]

Here is thing with Boltzmann brains and Poincare recurrence it is a highly Specualtive theory that relies heavily on the detail that there is a statistical possibility of occurance. However given the timeliness involved that are a great many orders of magnitude beyond the age of the Universe that likelyhood is incredibly low.

I mean, the probability of recurrence is of course extremely low, but assuming that the universe goes on forever and the cosmological constant does not evolve, then shouldn't this happen? I mean, of course we don't know if the assumptions I just made do happen, but if they are met, then doesn't the recurrence problem occur?

That should help you answer your own question regarding how a ground state when you introduce some further quantum fluctuation to your systems/states described by those papers can lead to higher energy states particularly if a small fluctuation expands throughout the system and potentially lead to further fluctuations.
The above can also give rise to particle creation/annihilation events. For example the number density of any particle species can be estimated by the blackbody temperature of the CMB via the Einstein Boltzmann statistics for bosons and the Fermi-Statistics for fermions.

But as I understand it, in this case the energy from the vacuum is "transferred", so that after a vacuum decay from a metastable state, the vacuum has now zero energy but this event generates a lot of energy in the universe (like, as you said, as particle-antiparticle annihilations), so now, although the universe can have now a lot of (e.g. thermal) energy and matter, the vacuum now has none. I guess my question is, can this be reversed?

It probably is an inaccurate picture, but I think of it as this example: Imagine having a room containing a perfectly isolated box which has a high temperature inside of it and then opening it (which would be the vacuum down-tunneling). The heat from the box would dissipate throughout the room, so now the room increases the temperature, but now the box doesn't have a higher temperature than the room, so the heat has been "transferred" from the box to the general room. However, assuming there are no heat losses, that heat will stay in the room indefinitely. Could there be a quantum fluctuation (no matter how unlikely as long as it has a non-zero probability) which causes the heat to return to the box, reaching back the initial state?

That should help you answer your own question regarding how a ground state when you introduce some further quantum fluctuation to your systems/states described by those papers can lead to higher energy states particularly if a small fluctuation expands throughout the system and potentially lead to further fluctuations.

That should help answer how a ground state under a field treatment that employs the momentum terms (mass, energy) can alter from the ground state to a different energy value. The requirement being potential field differences between any two or more reference points

So does this mean that if we have a field which employs the momentum terms (like mass or energy) it can alter the ground state of the universe to a higher energy value? Put in another way, as we have fields describing mass and energy in the universe, can they induce the ground state to be at a higher energy value via a rare quantum fluctuation?

 

[Mordred]

Yes the statistical possibility exists that's what your papers describe. Universe from nothing models in point of detail uses quantum fluctuations for the BB conditions which is one of the primary reasons those articles employ inflationary models such as Chaotic eternal inflation.
If you look into runaway inflation you will notice Chaotic eternal inflation can lend itself to Bubble universes. There is an an entire class of models (multiverse models) that uses the above process.

Though modern treatments of inflation now use slow roll parameters to allow inflation a graceful exit to resolve the runaway inflation issue.

 

[Suekdccia]

Yes the statistical possibility exists that's what your papers describe. Universe from nothing models in point of detail uses quantum fluctuations for the BB conditions which is one of the primary reasons those articles employ inflationary models such as Chaotic eternal inflation.
If you look into runaway inflation you will notice Chaotic eternal inflation can lend itself to Bubble universes. There is an an entire class of models (multiverse models) that uses the above process.

Though modern treatments of inflation now use slow roll parameters to allow inflation a graceful exit to resolve the runaway inflation issue.

But inflation requires the existence of the inflaton field which we don't know if it exists

Can it occur (theoretically in principle) with the fields and the forms of matter and energy that we know that exist?

 

[Mordred]

The inflaton is only one common version of inflation there is over 75 currently viable inflationary models some use the inflaton others don't. For example Higgs inflation.

Here is an article that runs comparisons for existing viable models. (There may be others the paper doesn't include)

Encyclopaedia Inflationaris

https://arxiv.org/abs/1303.3787

 

[Suekdccia]

The inflaton is only one common version of inflation there is over 75 currently viable inflationary models some use the inflaton others don't. For example Higgs inflation.

Here is an article that runs comparisons for existing viable models. (There may be others the paper doesn't include)

Encyclopaedia Inflationaris

https://arxiv.org/abs/1303.3787

And in slow roll inflation models would it be impossible to have another inflation event once it happens?

Also, referring to percolating vacuum bubbles again (which as far as I know are not necessarily related to inflation, but correct me if I'm wrong):

Consider a universe with a non-zero vacuum energy which undergoes vacuum decay and ends up in a true vacuum state. Just confirm then, so if I understood you correctly, if we'd wait essentially forever there could be a point where a random quantum fluctuation could make this universe with zero vacuum energy turn back into one with non-zero vacuum energy (or a non zero cosmological constant).

But it is still not clear to me whether to do so, the quantum flucutuation can make it without any energy or mass (i.e. making it happen in an empty universe without energy and mass, only spacetime, which seems wrong to me)? Or whether it requires that the universe must have energy (in any of its forms, like thermal energy for instance) or mass?

Which one is correct (if any)?

And also, what I get from your last post (#15) is that this can happen (in principle) with the fields and particles that we know that do exist, correct?

 

[Mordred]

The vacuum bubble questions depend on which inflationary model. A true vacuum could in theory go to a true vacuum to a false vacuum but the probability of ever occurring are incredibly low (see your links for examples)

In order to have a field of any form regardless of the average energy/mass density conservation laws still applies so yes the region must contain energy/mass. Particularly with closed systems such as a bubble (contained)

Yes this can occur regardless of particle type (quasi ie inflaton) or SM particles. The key is the mean average distribution

 

[Suekdccia]

The vacuum bubble questions depend on which inflationary model. A true vacuum could in theory go to a true vacuum to a false vacuum but the probability of ever occurring are incredibly low (see your links for examples)

In order to have a field of any form regardless of the average energy/mass density conservation laws still applies so yes the region must contain energy/mass. Particularly with closed systems such as a bubble (contained)

Yes this can occur regardless of particle type (quasi ie inflaton) or SM particles. The key is the mean average distribution

mmmh but in those slow roll inflationary models that escape runaway inflation that you mentioned, do they suppress it (making it even more unlikely) or do they directly eliminate that possibility (turning it into a 0 probability event)?

Regarding the explanation that you gave in your previous post (#17) then, if we consider a universe with a certain amount of mass/energy (considering fields that we know that do exist) distributed with enough density at some part of it, there could be eventually a very rare quantum fluctuation that could cause it to up-tunnel to a higher energy vacuum, correct?

 

[Mordred]

Early inflation models suffered runaway inflation . Models with slow roll attempt to stop inflation via the slow roll.
However Chaotic eternal inflation (eternal states lasts forever).

Wiki has a not too bad coverage
https://en.m.wikipedia.org/wiki/Eternal_inflation

So once again the answer depends on model. You may have noted the articles you linked use the latter case.

As to the last question the answer is yes but it's extremely unlikely hence the timelines of the probability functions of your articles.

 

[Suekdccia]

Early inflation models suffered runaway inflation . Models with slow roll attempt to stop inflation via the slow roll.
However Chaotic eternal inflation (eternal states lasts forever).

Wiki has a not too bad coverage
https://en.m.wikipedia.org/wiki/Eternal_inflation

So once again the answer depends on model. You may have noted the articles you linked use the latter case.

Ah, so the eternal chaotic inflation models arised from slow roll ones?

As to the last question the answer is yes but it's extremely unlikely hence the timelines of the probability functions of your articles.

And could such unlikely (but with non-zero probability) quantum fluctuations occur in slow-roll inflation models as well?


Also, I have 2 final questions about this then:

1. Then from your explanation about quantum fluctuations and up-tunneling events I understand that this is a very different mechanism from the one depicted in (https://arxiv.org/abs/2301.03620) where it was about cosmic rays. So while a quantum fluctuation causing an up-tunneling is very unlikely (and it would occur in enormous timescales) it is not suppressed in the same sense as in the cosmic ray collision scenario (where the author said that because of this it was nearly impossible to occur by itself in nature), right?

2. So if a very rare quantum fluctuation could cause an up-tunneling event of the vacuum in a zone where a mass/energy field has enough density, can you estimate approximately and roughly how much mass or energy density would be needed?

 

[Mordred]

Yes to each question above with regards to the last question the answer would depend on the bubble involved. The process is possible even with slow roll.

 

[Suekdccia]

Yes to each question above with regards to the last question the answer would depend on the bubble involved. The process is possible even with slow roll.

Regarding the last question, would there be any amount of mass/energy field density that would be enough to occur under any scenario? Is there any estimation of it?

 

[Mordred]

Let's put it this way it took a state condition of 10^{19} GeV to form our Observable universe. That's just for our Observable universe. We do not know how large the entire universe is. There could very well be other regions with different expansion rates outside our Observable portion that we will never have direct evidence for.
Some regions could very well be collapsing while others expanding we will never know through direct observation but it's a viable possibility.
That's a detail that is described by your papers as well.
You only require different energy/mass densities from one region to another to get different expansion/collapsing regions.

 

[Suekdccia]

Let's put it this way it took a state condition of 10^{19} GeV to form our Observable universe. That's just for our Observable universe. We do not know how large the entire universe is. There could very well be other regions with different expansion rates outside our Observable portion that we will never have direct evidence for.
Some regions could very well be collapsing while others expanding we will never know through direct observation but it's a viable possibility.
That's a detail that is described by your papers as well.
You only require different energy/mass densities from one region to another to get different expansion/collapsing regions.

Mmmh I think I meant a slightly different thing:

So, to sum up our conversation, for a universe (or at least a region of it) to up-tunnel from a true vacuun energy to a higher one, if we assume that time and that this universe are endless, there would be some time in the extremely far future where a very rare quantum fluctuation could make this up-tunneling event possible.

However, as you said in post #17 for this to occur in some region of the universe, that region must have at least some energy/mass density.

Then I asked in post #20 how much energy/mass density would be needed for a quantum fluctuation to make that region up-tunnel into a higher vacuum energy level. You told me in post #21 that this would depend on the type of vacuum bubble involved.

So in post #22 what I was asking was rather:

What would be an estimation of the minimum energy/mass density that a region of the universe should have so that in the very far future a rare quantum fluctuation could make it up-tunnel to a higher vacuum energy level?

Or put in another way

Is there some minimum energy/mass density of a region of the universe in which a rare quantum fluctuation could make it up-tunnel to a higher vacuum energy level that would work for every type of bubble involved? Some minium energy/mass density in a region of thr universe that would work for every possible bubble no matter the type?

 

[Mordred]

There isn't a miscommunication think back to the article you posted above.
https://arxiv.org/pdf/1005.3506

So lets take from this article vacuum bubble A that collides with vacuum bubble b and results in vacuum bubble C.

What occurs depends on the energy differences between bubble A and bubble B. When you use the format here you recognize that the zero point is not the same as zero energy. If you recall it's a non zero value set at zero. In some of the examples the vacuum is positive in one region while negative in another. (Recall vacuum is being describes by the kinetic vs potential energy relations) ie negative vacuum the particles kinetic energy exceeds the regions potential energy terms. Reverse is true for a positive vacuum

So all you need is some potential and kinetic energy differences between the two regions. Your asking if there is some minimal energy requirement when the only requirement is there must be some potential and kinetic energy differences between the two regions.

In essence some difference between the two vacuum bubbles if the two vacuum bubbles are identical nothing happens. In every other case a change will occur resulting in a new vacuum bubble C. What the vacuum conditions of C will be will depend on the the interaction between A and B and the conditions of both vacuum bubbles

Also recognize that due to the quantum harmonic oscillator described by QM you can never have an absolute zero energy density. ( you always have quantum fluctuations its unavoidable) QM teaches us that. The zero point isn't a true zero it is the global mean average set as zero. That global value could be positive or negative vacuum (still has positive energy density however miniscule) example our universe the global energy density is described using the critical density formula of the FLRW metric a rough order calculation will give the energy density as 7 ×10^{-10} joules/cubic metre. Combined with the scalar field equation of state formula a negative vacuum (kinetic vs potential energy terms) in our universe today largely due to the cosmological constant term.

the scalar field equation of state formula is as follows.
$\omega=\frac{1/2 \dot{\phi}^2-V\phi}{1/2 \dot{\phi}^2+V\phi}$
where $V\phi$ is the potential energy term.
the overdot is a time derivative in this case the velocity term.

https://en.wikipedia.org/wiki/Time_derivative

put simply region A for example w=0.75 region B=-1. You have a difference between A and B but that difference is described by the above formula where the -1 and 0.75 values are not energy density values. Those are contained in the formula the resultant w itself doesn't have any units.
Now consider further the w term could be identical lets say w=-1 in both cases but the energy densities involved could still be different between the two. (for example in our universe past the mean average energy density is greater than 7*10^{-10} joules/cubic meter)
here is the critical density formula.
$\rho_{crit}=\frac{3c^2H^2}{8\pi G}$

there isn't some minimal value or maximum value involved the only requirement is that Vacuum A must have some difference from Vacuum B in either the potential or the kinetic energy terms or the energy density. You can have two regions of identical energy density but different potential energy and kinetic energy relations and get a new vacuum term either a new false vacuum state or a new true vacuum state. It all depends on the interaction between the two vacuum bubbles and what is distinct between the two.

Let's take another example you have our universe which could be described as an Anti-Desitter bubble and that bubble encounters a DeSitter bubble both can have identical energy density but as one is anti-Desitter while the other is positive you will still get a new vacuum bubble C.

Remember that due to the Quantum harmonic oscillator you have some non zero energy density (absolute zero is impossible due to this)

https://en.wikipedia.org/wiki/Equation_of_state_(cosmology)

I should also note that a DeSitter space and an anti-Desitter space also include the scalar curvature term
https://en.wikipedia.org/wiki/De_Sitter_space
https://en.wikipedia.org/wiki/Anti-de_Sitter_space

the distinction between the two can be described by that equation of state formula above.
if w<0 its negative vacuum if w>0 its positive vacuum however that is a ratio value given by that formula.

When you see the description negative energy density that descriptive is a bit of a misnomer its in essence a bit lazy. Its really referring to a positive energy density of a state with negative vacuum defined by w from the formula above.
In essence you must understand what the term vacuum really entails its not specifically energy density. It is defined by the equations of state involved and their potential vs kinetic energy terms

 

[Mordred]

Now take the above with regards to phase transitions. Ask yourself what occurs for example during electroweak symmetry breaking ? The Higgs field couples to leptons giving us a mass term. So the potential and kinetic energy terms change as a result. A new phase transition would imply new couplings or new coupling values leading to a new vacuum state.
Thinking of vacuum strictly in energy density terms is incorrect it is a relation described above.

 

[Suekdccia]

There isn't a miscommunication think back to the article you posted above.
https://arxiv.org/pdf/1005.3506

So lets take from this article vacuum bubble A that collides with vacuum bubble b and results in vacuum bubble C.

What occurs depends on the energy differences between bubble A and bubble B. When you use the format here you recognize that the zero point is not the same as zero energy. If you recall it's a non zero value set at zero. In some of the examples the vacuum is positive in one region while negative in another. (Recall vacuum is being describes by the kinetic vs potential energy relations) ie negative vacuum the particles kinetic energy exceeds the regions potential energy terms. Reverse is true for a positive vacuum

So all you need is some potential and kinetic energy differences between the two regions. Your asking if there is some minimal energy requirement when the only requirement is there must be some potential and kinetic energy differences between the two regions.

In essence some difference between the two vacuum bubbles if the two vacuum bubbles are identical nothing happens. In every other case a change will occur resulting in a new vacuum bubble C. What the vacuum conditions of C will be will depend on the the interaction between A and B and the conditions of both vacuum bubbles

Also recognize that due to the quantum harmonic oscillator described by QM you can never have an absolute zero energy density. ( you always have quantum fluctuations its unavoidable) QM teaches us that. The zero point isn't a true zero it is the global mean average set as zero. That global value could be positive or negative vacuum (still has positive energy density however miniscule) example our universe the global energy density is described using the critical density formula of the FLRW metric a rough order calculation will give the energy density as 7 ×10^{-10} joules/cubic metre. Combined with the scalar field equation of state formula a negative vacuum (kinetic vs potential energy terms) in our universe today largely due to the cosmological constant term.

the scalar field equation of state formula is as follows.
$\omega=\frac{1/2 \dot{\phi}^2-V\phi}{1/2 \dot{\phi}^2+V\phi}$
where $V\phi$ is the potential energy term.
the overdot is a time derivative in this case the velocity term.

https://en.wikipedia.org/wiki/Time_derivative

put simply region A for example w=0.75 region B=-1. You have a difference between A and B but that difference is described by the above formula where the -1 and 0.75 values are not energy density values. Those are contained in the formula the resultant w itself doesn't have any units.
Now consider further the w term could be identical lets say w=-1 in both cases but the energy densities involved could still be different between the two. (for example in our universe past the mean average energy density is greater than 7*10^{-10} joules/cubic meter)
here is the critical density formula.
$\rho_{crit}=\frac{3c^2H^2}{8\pi G}$

there isn't some minimal value or maximum value involved the only requirement is that Vacuum A must have some difference from Vacuum B in either the potential or the kinetic energy terms or the energy density. You can have two regions of identical energy density but different potential energy and kinetic energy relations and get a new vacuum term either a new false vacuum state or a new true vacuum state. It all depends on the interaction between the two vacuum bubbles and what is distinct between the two.

Let's take another example you have our universe which could be described as an Anti-Desitter bubble and that bubble encounters a DeSitter bubble both can have identical energy density but as one is anti-Desitter while the other is positive you will still get a new vacuum bubble C.

Remember that due to the Quantum harmonic oscillator you have some non zero energy density (absolute zero is impossible due to this)

https://en.wikipedia.org/wiki/Equation_of_state_(cosmology)

I should also note that a DeSitter space and an anti-Desitter space also include the scalar curvature term
https://en.wikipedia.org/wiki/De_Sitter_space
https://en.wikipedia.org/wiki/Anti-de_Sitter_space

the distinction between the two can be described by that equation of state formula above.
if w<0 its negative vacuum if w>0 its positive vacuum however that is a ratio value given by that formula.

When you see the description negative energy density that descriptive is a bit of a misnomer its in essence a bit lazy. Its really referring to a positive energy density of a state with negative vacuum defined by w from the formula above.
In essence you must understand what the term vacuum really entails its not specifically energy density. It is defined by the equations of state involved and their potential vs kinetic energy terms

Oh, I see

So when you talk about the kinetic and potential energy terms in the universe (or at least a region of it) are you referring to its objects' kinetic energy (essentially the velocity) and the gravitational potential energy of objects respectively?

In any case, this explanation is considering the situation of vacuum bubbles colliding to form new bubbles. But what about a single vacuum undergoing an extremely rare quantum fluctuation that would make it up-tunnel to a higher vacuum energy? Would we only need to consider the differences between the kinetic and potential energies of that initial vacuum?

 

[Mordred]

The multi particle system as opposed to objects. For example photons or massless particles such as the quasi particle inflaton.
For potential energy the field couplings

For single vacuum you could get higher vacuum conditions if the bubble starts collapsing which you would still have a conserved system other than that I can't of any example that does not require additional energy being added to the bubble. At least with regards to the entirety of the bubble. Your cosmic rays would be a smaller bubble region inside a larger bubble where the smaller bubble expands (bubble nucleation)

 

[Suekdccia]

The multi particle system as opposed to objects. For example photons or massless particles such as the quasi particle inflaton.
For potential energy the field couplings

For single vacuum you could get higher vacuum conditions if the bubble starts collapsing which you would still have a conserved system other than that I can't of any example that does not require additional energy being added to the bubble. At least with regards to the entirety of the bubble. Your cosmic rays would be a smaller bubble region inside a larger bubble where the smaller bubble expands (bubble nucleation)

Would we be also considering moving particles like protons or electrons travelling throughout the universe in the multi particles system? And what would be exactly the field couplings?

Regarding the second part:

So if I understood it right, there could be cases where if the kinetic+potential energy terms were in the right range, a rare quantum fluctuation would cause a vacuum bubble which could immediately collapse and if this happens the universe would up-tunnel to a higher vacuum energy?

Also when you say

other than that I can't of any example that does not require additional energy being added to the bubble. At least with regards to the entirety of the bubble

Couldn't that additional energy come from the energy content of the universe itself? I mean, couldn't some very rare quantum fluctuation "use" the energy content of some region of the universe (consider a region with a high energy density in any of its forms: kinetic, potential, thermal...) in order to make the universe go up to a higher vacuum energy level?

 

[Suekdccia]

Also apart from the previous questions that I made, after reading again your last post and doing some more reading about the topic I had some brief additional questions:

Could a down-tunneling and up-tunneling event occur even if two vacua (for instance a false and a true vacua) are very close to each other in vacuum energy density? I ask you this because according to this paper by Sidney Coleman (https://ui.adsabs.harvard.edu/abs/1980PhRvD..21.3305C/abstract) if two vacua have very small differences in their vacuum energy then they won't tunnel. However, in these other papers (https://arxiv.org/abs/hep-th/0302062 and https://journals.aps.org/prd/abstract/10.1103/PhysRevD.99.016016 page 9) the authors talk about tunneling events between vacua of very similar vacuum energy. So do you know if it is possible or not?

Also, could a vacuum down tunneling or up tunneling occur in a slow and progressive manner instead of a singular and strong event like a vacuum bubble? For example, in this paper (https://arxiv.org/pdf/2310.06901) the authors seem to suggest that black holes may cause a soft and progressive transition (however they are talking about phase transitions so I'm not sure if they mean what I mean when I'm thinking about the vacuum changing into another vacuum with a different vacuum energy but with a slow and progressive process instead of a sudden one)