Exactly how quantum tunneling leads to a Big Bang?

[Rodrigo Olivera]

In wikipedia says that in a big amount of time quantum tunneling can create a new Big Bang. EXACTLY, how this happens.
https://en.wikipedia.org/wiki/Future_of_an_expanding_universe ("Beyond" part)
*note: I'm in high school, but feel free to explain this with complicate process.

 

[Orodruin]

Please provide the page where you read this. How else are we supposed to know exactly what you read and whether it is a problem of the text itself or your understanding of it? "Read on Wikipedia" is not a valid reference here.

 

[Rodrigo Olivera]

https://en.wikipedia.org/wiki/Future_of_an_expanding_universe ("Beyond" part)

 

[stoomart]

https://en.wikipedia.org/wiki/Future_of_an_expanding_universe ("Beyond" part)

Here's the referenced paper (page 20-21): Spontaneous Inflation and the Origin of the Arrow of Time.

 

[Rodrigo Olivera]

Here's the referenced paper (page 20-21): Spontaneous Inflation and the Origin of the Arrow of Time.

Exactly, in which part says how quantum tunneling lead a new big bang?

 

[stoomart]

Exactly, in which part says how quantum tunneling lead a new big bang?

In this case I put the specific page numbers in parentheses, the search button is your friend. : )

Edit: You will learn on these forums that the term "Big Bang" is usually synonymous with "inflation".

 

[PeterDonis]

You will learn on these forums that the term "Big Bang" is usually synonymous with "inflation".

No, it isn't. In inflationary models, the Big Bang is the hot, dense, rapidly expanding state of the universe after inflation ends.

 

[stoomart]

No, it isn't. In inflationary models, the Big Bang is the hot, dense, rapidly expanding state of the universe after inflation ends.

If it's not too off-topic, I have a couple questions to hopefully clarify my understanding from the pop-sci/Wikipedia mire, and the expert information discussed here on PF:

Is there a more technical term for that state than "Big Bang" (Wikipedia articles say "reheating/thermalization" comes after inflation)?
Are there size estimates for how small and large the universe was at the beginning and end of the inflationary period or is that irrelevant?

The exponential expansion of the inflationary period seems more bang-like than rapid (though decelerating) expansion. But the more I read about this, it sounds like inflation was a "fix" for problems realized in early Big Bang cosmology, and is a necessary bridge between the Big Bang singularity and the Big Bang state.

 

[Drakkith]

The problem is that the term "big bang" is not a technical description, but an offhand name given by an opponent of the initial theory. The term has come to have several different meanings:

1. The absolute beginning of the universe. Prior to inflation, prior to everything.
2. The initial expansion in non-inflationary cosmology without regard to what may have causes this expansion nor what may have come before it. In this sense the big bang wasn't the creation of the universe, but merely the initial phase of rapid expansion.
3. The rapid expansion after inflation ends (which is an expansion process, but one of a different nature than the big bang in this context).

Exactly, in which part says how quantum tunneling lead a new big bang?

I'm not quite sure, but I think there is an absolutely tiny, but non-zero, probability for all particles in the universe to quantum tunnel to a location and state similar to that of the very early universe. So instead of matter being spread very thinly throughout all of space (on average), it would tunnel to a state where all matter is highly compressed and very hot, similar to the conditions of the very early universe. Someone correct me if I'm wrong please.

 

[stoomart]

Thanks for the explanation @Drakkith, it sounds like my understanding was based on #2.

From the paper:

Garriga and Vilenkin, for example, have proposed that thermal fluctuations can induce tunneling from a true de Sitter vacuum to a false vacuum at higher energies, thus inducing spontaneous inflation.
...
We believe that the resulting number (which is fantastically small) provides a sensible minimum value for the probability to fluctuate up into inflation.

 

[PeterDonis]

I think there is an absolutely tiny, but non-zero, probability for all particles in the universe to quantum tunnel to a location and state similar to that of the very early universe. So instead of matter being spread very thinly throughout all of space (on average), it would tunnel to a state where all matter is highly compressed and very hot, similar to the conditions of the very early universe.

From the paper:

My understanding is different. As I understand it, the tunneling in question is from a very tiny piece of ordinary vacuum--similar to the kind we have in empty space we're familiar with (note that this vacuum must have a tiny but nonzero cosmological constant, that's what the "true de Sitter vacuum" in the quote stoomart gave refers to)--to a very tiny piece of "false vacuum", i.e., a very tiny piece of the kind of stuff that undergoes inflation (in the cosmological sense). The very tiny piece of false vacuum will then inflate, creating a new universe.

Some versions of inflationary cosmology say that this is how our universe began--that there is a sort of "background" spacetime that is always in the true de Sitter vacuum state, but due to thermal fluctuations every so often a tiny piece of false vacuum appears and inflates, and one of those tiny pieces is the piece that formed our universe.

Another model says that the true de Sitter vacuum is the end state of every universe, and once it gets to that end state, sooner or later a thermal fluctuation will create a tiny piece of false vacuum and the whole inflation cycle starts again.

AFAIK none of these models are experimentally testable at this point.

 

[Drakkith]

Ah, well, I certainly trust your understanding more than mine.

 

[stoomart]

The following statement in the paper indicates the tunneling model is not preferred, is that still the case?

In our discussion is that we examine the case of an harmonic oscillator potential without any false vacua; in such a potential we can simply fluctuate up without any tunneling. The resulting period of inflation can then end via conventional slow-roll, which is more phenomenologically acceptable than tunneling from a false vacuum (as in “old inflation” [7]). Thus, the emptying-out of the universe under typical evolution of a generic state can actually provide appropriate initial conditions for the onset of inflation, which then leads to regions that look like our universe.

References Phys. Rev. D 23, 347: Inflationary universe: A possible solution to the horizon and flatness problems

 

[PeterDonis]

The following statement in the paper indicates the tunneling model is not preferred, is that still the case?

As I understand it, "slow roll" models that do not involve tunneling are currently preferred in inflationary cosmology, yes.

 

[stoomart]

Thanks guys, learned a lot.

 

[Rodrigo Olivera]

My understanding is different. As I understand it, the tunneling in question is from a very tiny piece of ordinary vacuum--similar to the kind we have in empty space we're familiar with (note that this vacuum must have a tiny but nonzero cosmological constant, that's what the "true de Sitter vacuum" in the quote stoomart gave refers to)--to a very tiny piece of "false vacuum", i.e., a very tiny piece of the kind of stuff that undergoes inflation (in the cosmological sense). The very tiny piece of false vacuum will then inflate, creating a new universe.

Some versions of inflationary cosmology say that this is how our universe began--that there is a sort of "background" spacetime that is always in the true de Sitter vacuum state, but due to thermal fluctuations every so often a tiny piece of false vacuum appears and inflates, and one of those tiny pieces is the piece that formed our universe.

Another model says that the true de Sitter vacuum is the end state of every universe, and once it gets to that end state, sooner or later a thermal fluctuation will create a tiny piece of false vacuum and the whole inflation cycle starts again.

AFAIK none of these models are experimentally testable at this point.

I didn't understand well the part of how quantum tunneling leads to a inflation. You said that the tunneling is similar to a vacumm or a tiny "false vacuum", but HOW does this piece of false vacuum inflate. (ok, by quantum tunneling, but HOW).*By the way, I really appreciate the answers.

 

[PeterDonis]

HOW does this piece of false vacuum inflate. (ok, by quantum tunneling

No, it doesn't inflate by quantum tunneling. Quantum tunneling just creates the tiny piece of false vacuum (at least, according to the hypothesis under discussion--none of this has been tested experimentally). The false vacuum inflates because of the properties of the particular quantum field--an "inflaton" field--that it is a false vacuum state of; these properties are basically like those of a large positive cosmological constant, i.e., they cause exponential expansion with a very short time constant.

 

[Rodrigo Olivera]

No, it doesn't inflate by quantum tunneling. Quantum tunneling just creates the tiny piece of false vacuum (at least, according to the hypothesis under discussion--none of this has been tested experimentally). The false vacuum inflates because of the properties of the particular quantum field--an "inflaton" field--that it is a false vacuum state of; these properties are basically like those of a large positive cosmological constant, i.e., they cause exponential expansion with a very short time constant.

How does quantum tunneling creates that tiny peace of false vacuum? I'm sorry if I very insistent with this, but I have to made a monograph explaining this.

 

[PeterDonis]

How does quantum tunneling creates that tiny peace of false vacuum?

In the hypothesis under discussion (which, I stress once again, is just a hypothesis and hasn't been experimentally tested, and can't really be experimentally tested with our current technology), it's the reverse of the process that ends inflation in the original "old inflation" models (like the one Alan Guth originally proposed). You have two possible vacuum states of the field, the "false vacuum" and the "true vacuum". If the field is in either state, there is a small probability for it to quantum tunnel into the other.

I have to made a monograph explaining this.

Then you should be doing a lot more research than just asking questions here. You need to be looking at textbooks and peer-reviewed papers. Plenty of them.

 

[Rodrigo Olivera]

In the hypothesis under discussion (which, I stress once again, is just a hypothesis and hasn't been experimentally tested, and can't really be experimentally tested with our current technology), it's the reverse of the process that ends inflation in the original "old inflation" models (like the one Alan Guth originally proposed). You have two possible vacuum states of the field, the "false vacuum" and the "true vacuum". If the field is in either state, there is a small probability for it to quantum tunnel into the other.
Then you should be doing a lot more research than just asking questions here. You need to be looking at textbooks and peer-reviewed papers. Plenty of them.

I have clear that this is just an hypothesis. But I don´t have yet a clear answer, HOW does quantum tunneling turn a false vacuum to a true vacuum, and vice versa.

Don't worry about the investigation, I have 17 sources but non of them explain me this.

 

[stoomart]

I have clear that this is just an hypothesis. But I don´t have yet a clear answer, HOW does quantum tunneling turn a false vacuum to a true vacuum, and vice versa.

Don't worry about the investigation, I have 17 sources but non of them explain me this.

What sources do you have for quantum tunneling? (I haven't read any on it, but would like to)

 

[PeterDonis]

HOW does quantum tunneling turn a false vacuum to a true vacuum, and vice versa.

Quantum tunneling doesn't turn one vacuum into the other. The two vacua are two possible states of the quantum field, with a potential energy barrier between them. As with any quantum system with two states separated by a potential energy barrier, there is a probability for the system to quantum tunnel from one of the two states to the other. That's all there is to it.

 

[Rodrigo Olivera]

Quantum tunneling doesn't turn one vacuum into the other. The two vacua are two possible states of the quantum field, with a potential energy barrier between them. As with any quantum system with two states separated by a potential energy barrier, there is a probability for the system to quantum tunnel from one of the two states to the other. That's all there is to it.

Okay, now I understand. But a true vacuum it is assumed that is a sphere that grows at the speed of light in all directions changing the laws of physics, and this can happen anytime. A true vacuum can't create another universe, but a false vacuum can by inflation (correct if I'm wrong). What does true vacuum have to do with this. I though that quantum tunneling causes the inflation of a false vacuum because of potencial energy.

stoomart you can check this video:

 

[stoomart]

The takeaway from this thing for me was to look at bubble nucleation, which seems to be the most technical explanation (from non-published sources) for your "HOW" questions.

 

[PeterDonis]

a true vacuum it is assumed that is a sphere that grows at the speed of light in all directions changing the laws of physics

Changing some particular physical constants in the Standard Model laws, yes. But the Standard Model laws, in this picture, are not the fundamental laws; they emerge from the fundamental laws under particular conditions. The fundamental laws do not change.

Also, the true vacuum "bubble" inside a false vacuum will expand this way; but so will a bubble of false vacuum inside a true vacuum.

Finally, thinking of the bubble expanding "at the speed of light" can be misleading. It can be thought of that way looking at the bubble from the outside, but not from the inside.

A true vacuum can't create another universe, but a false vacuum can by inflation

This is not correct. See what I said above about bubbles. "Creating another universe" can be applied to either case: a bubble of true vacuum forming inside a false vacuum and then expanding (this case is like the end of inflation in the "old inflation" cosmology), or a bubble of false vacuum forming inside a true vacuum and expanding (this case is like the start of inflation in the "quantum tunneling creates a new inflating bubble" scenario).

 

[Rodrigo Olivera]

Changing some particular physical constants in the Standard Model laws, yes. But the Standard Model laws, in this picture, are not the fundamental laws; they emerge from the fundamental laws under particular conditions. The fundamental laws do not change.

Also, the true vacuum "bubble" inside a false vacuum will expand this way; but so will a bubble of false vacuum inside a true vacuum.

Finally, thinking of the bubble expanding "at the speed of light" can be misleading. It can be thought of that way looking at the bubble from the outside, but not from the inside.
This is not correct. See what I said above about bubbles. "Creating another universe" can be applied to either case: a bubble of true vacuum forming inside a false vacuum and then expanding (this case is like the end of inflation in the "old inflation" cosmology), or a bubble of false vacuum forming inside a true vacuum and expanding (this case is like the start of inflation in the "quantum tunneling creates a new inflating bubble" scenario).

Now I understand, just two last things that I would really appreciate:

1.- Big Bang theory mantains that in before the everywhere stretching (big bang) all matter was condense in a small piece of hot space, Where the curvatures manifests itself as a rapid expansion. Suposing that quantum tunneling , false and true vacuum and thermal fluctuations are true and will happen, how will the universe would start again, I mean, all matter is separated, not together and condense in a small piece like in the big bang singularity.

2.- I want to use the information you leave here by quoting you. Could give some information (or sources) about your career, like your name, the university you studied and your tittle. I need to confirm you're a primary source.

Thanks for clear my doubts.

 

[PeterDonis]

Suposing that quantum tunneling , false and true vacuum and thermal fluctuations are true and will happen, how will the universe would start again

A small piece of true vacuum quantum tunnels into a small piece of false vacuum. The false vacuum inflates.

all matter is separated, not together and condense in a small piece like in the big bang singularity

First, in the models we are talking about here, there is no "big bang singularity". The "big bang" is the hot, dense, rapidly expanding state that a new universe is in just after inflation ends--i.e., just after a small piece of false vacuum quantum tunnels into a small piece of true vacuum.

Second, in the case just described, just before the small piece of false vacuum quantum tunnels into the small piece of true vacuum, there is no hot, dense, rapidly expanding matter. The new universe is empty--there are no particles in the false vacuum state. (That's why it's called a "vacuum".) After the small piece of false vacuum quantum tunnels into the small piece of true vacuum, the energy that was in the false vacuum state, which is much larger than the energy in the true vacuum state it tunnels into, gets transferred into particles--the Standard Model particles like electrons and quarks and photons and so on. This creates the hot, dense, rapidly expanding state that is called the "big bang".

In the opposite case, where a small piece of true vacuum quantum tunnels into a small piece of false vacuum, a lot of energy has to be supplied, because, as above, the small piece of false vacuum has much more energy than the piece of true vacuum that quantum tunneled into it. So such an event will be very rare in a universe like ours, because it can only happen if a thermal fluctuation concentrates enough energy into a very small volume to enable the tunneling to happen.

I want to use the information you leave here by quoting you

Don't. I'm not a valid primary source. Use actual textbooks or peer-reviewed papers.

 

[Rodrigo Olivera]

Don't. I'm not a valid primary source. Use actual textbooks or peer-reviewed papers.

Well, do you have some sources that you can post here about this topics? I would thank you so much

 

[PeterDonis]

do you have some sources that you can post here about this topics?

Not at the moment. I would suggest looking for papers on inflationary cosmology. Guth, Linde, and Vilenkin are good authors to start with.

 

[haushofer]

I really like

Quantum cosmology for pedestrians - Quantum Gravity & Ground State Energy

by Atkatz.