# Inflationary vacuum and the true vacuum

## Main Question or Discussion Point

In a review of particle-theory models of inflation by D.H.lyth and A.riotto
http://au.arxiv.org/abs/hep-ph/9807278, they talked about the true vacuum and the inflationary vacuum in page 45, but I have not understand well the difference between them.
Could someone clarify the difference between them?

In a review of particle-theory models of inflation by D.H.lyth and A.riotto
http://au.arxiv.org/abs/hep-ph/9807278, they talked about the true vacuum and the inflationary vacuum in page 45, but I have not understand well the difference between them.
Could someone clarify the difference between them?
Wald says of curved spacetimes that particles are undefinable in highly curved spacetimes. One reason for expecting Inflation is to explain the flatness of the universe from a very tightly compact ball, presumably with very tightly curved space. So I have to wonder if particles even existed during Inflation since the space was so curved that particles could not be unambiguously defined.

Wald says of curved spacetimes that particles are undefinable in highly curved spacetimes. One reason for expecting Inflation is to explain the flatness of the universe from a very tightly compact ball, presumably with very tightly curved space. So I have to wonder if particles even existed during Inflation since the space was so curved that particles could not be unambiguously defined.
In fact I am still a beginner in inflation, but I will answer you according to how much I know.
During Inflation, the universe is expanding very rapidly(exponentially) and the number of any existed particled decays exponentially.

In fact I am still a beginner in inflation, but I will answer you according to how much I know.
During Inflation, the universe is expanding very rapidly(exponentially) and the number of any existed particled decays exponentially.
They talk about the Inflaton scalar field oscillating after inflation. And this oscillations decay to give particles their mass. What I don't know is whether there are massless particles before the inflaton field decays, etc. Do photons exist all during inflation?

They talk about the Inflaton scalar field oscillating after inflation. And this oscillations decay to give particles their mass. What I don't know is whether there are massless particles before the inflaton field decays, etc. Do photons exist all during inflation?
During inflation the number of all particles including photons decays.
you can take look at the following paper page 8
http://www-spires.fnal.gov/spires/find/hep/www?rawcmd=find+t+particle+physics+aspects+of+modern+cosmology

hellfire
Inflation is based on a scalar field with a self-interaction potential. The state of the field at the absolute minimum of the potential is the true vacuum. The false or inflationary vacuum is a metastable state, that can correspond to a relative minimum of the potential. If the potential energy of a scalar field is dominant over its kinetic energy, it behaves as a cosmological constant accelerating the expansion of space. The article about False vacuum in wikipedia may help.

hellfire said:
Inflation is based on a scalar field with a self-interaction potential. The state of the field at the absolute minimum of the potential is the true vacuum.
Of course, but I think the question is what are the implication of the vacuum at any time. I don't think the universe in any way responded to the lower final state of affairs during the actual moments of Inflation. So the question is what does such a high vacuum state imply. One question I have is does this large vacuum state imply that the uncertainty principle was more uncertain then then now? The uncertainty principle is that delta E * delta t > h-bar/2. And this uncertainty in energy for a given time interval gives rise to the vacuum energy which may cause particles of a particular mass (=energy) to pop into existence for a brief moment. So if the vacuum energy were higher, then the energy of particles (if they exist) would be larger too for that same given time interval. Or alternatively this can be stated by saying that there is more uncertainty in the universe during Inflation than now. So I'm wondering if Inflation is a mechanism to reduce uncertainty in the universe.

It's a remarkable theory, inflation. But I like to pose some questions too.

From where or what do we assume that such a scalar field exist, and how do we define (and based on what?) it's properties.
Why is it a scalar field (and not some other field, like vector field, or something).

What about other fields? They don't exist?

Does the scalar field still exist?
Why doesn't inflation happen here and now? What would occur if inflation could happen here and now, would it overtake the current universe, or would it simply create a seperate spacetime, nonobservable to us?

What are the conditions for inflation to occur?

Hope someone can answer these questions.

hellfire
From where or what do we assume that such a scalar field exist, and how do we define (and based on what?) it's properties.
Scalar fields have not been observed yet, but they are a common assumption in modern physics (like the Higgs field, for example). The properties of the scalar field that drove inflation are postulated in order to lead to the correct inflationary scenario. For example, for models without tunneling the self-interacting pontential must be as flat as possible to allow for a slow-roll and an appropiate duration of the inflationary phase.

Why is it a scalar field (and not some other field, like vector field, or something).
Because scalar fields exert a negative pressure if their kinetic energy is negligible wrt the potential energy or vacuum energy. Negative pressure is responsible for the accelerated expansion that is needed during inflation.

What about other fields? They don't exist?
They exist but their energy density is negligible. The scalar field dominated the energy density at that stage.

Does the scalar field still exist?
Why doesn't inflation happen here and now?
The field is assumed to exist, but its energy density is negligible now.

What are the conditions for inflation to occur?
The scalar field with its appropiate self-interacting potential must be in a state in which its potential energy is high compared to its kinetic energy. In some quantum cosmology models, such as the tunneling proposal of Alexander Vilenkin, the unverse, comprised by space-time with a scalar field in a simplest model, is most likely to nucleate with the largest possible potential energy.

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Hellfire:

Yet another question, regarding vacuum states. I wonder from where comes the concept of a "true" vacuum. I mean, isn't that a very relative concept?

I have come across an idea about field theory in general, which generaly prescibes that field potentials are all relative, and not absolute.

To put it more concrete: all our electronic and electricity equipment would still work the same, no matter what the actual electric potential of earth would be. So a state of 0 electric field potential of earth, is just what we define it to be, but there is no way to tell what it actually is, nor does it matter.

(I don't know the english name for the theory, but in dutch it is called "ijkveld theorie" I guess it was invented by Eric van't Hooft, who also invented the holographic theory).

Isn't that also applicable to this scalar field potential in inflation cosmology, and which means, there is no real "true" vacuum?

hellfire
I am not sure to understand your question. The definition of (true) vacuum is related to the lowest energy and this corresponds to the absolute minimum of the potential. There must be an absolute minimum of the self-interacting potential regardless of the value of the vacuum energy at that state. Otherwise the vacuum would not be stable.

I am not sure to understand your question. The definition of (true) vacuum is related to the lowest energy and this corresponds to the absolute minimum of the potential. There must be an absolute minimum of the self-interacting potential regardless of the value of the vacuum energy at that state. Otherwise the vacuum would not be stable.
The potentials expressed in the potential field or scalar field, what are they?
What do they represent physically? Energy? Force? Some other physical entity?

And are the values absolutes or relative values?

Like my analogy of an electric potential field, there is no way in telling what the absolute value is, because it is only a relative measure.

What we call "earth" (zero electric potential) is just a definition, it could be any value, it would not matter for the electromagnetic theory, it all works the same.
That is to say, for all practical purposes and applications, the only thing what matters is the potential differences.

I am not sure to understand your question. The definition of (true) vacuum is related to the lowest energy and this corresponds to the absolute minimum of the potential. There must be an absolute minimum of the self-interacting potential regardless of the value of the vacuum energy at that state. Otherwise the vacuum would not be stable.
We don't know that we are at the bottom of the potential now. Some think inflation is eternal. And some think there may exist a phantom energy that will rip the universe apart.

hellfire
The potentials expressed in the potential field or scalar field, what are they?
What do they represent physically? Energy? Force? Some other physical entity?

And are the values absolutes or relative values?

Like my analogy of an electric potential field, there is no way in telling what the absolute value is, because it is only a relative measure.

What we call "earth" (zero electric potential) is just a definition, it could be any value, it would not matter for the electromagnetic theory, it all works the same.
That is to say, for all practical purposes and applications, the only thing what matters is the potential differences.
A self-interaction potential is same as any other, like for example when you analize a particle in a potential well or ball rolling down a hill. You are right that usually one is only interested in the potential energy difference between two points of the hill, for example. In quantum field theory things are similar. The vacuum energy is usually set to zero, and one can take all other energies relative to that one. However, this is not valid anymore if gravitation is taken into account. The value of the lowest energy cannot be set arbitrarily to zero because it may have an influence on space-time.

A self-interaction potential is same as any other, like for example when you analize a particle in a potential well or ball rolling down a hill. You are right that usually one is only interested in the potential energy difference between two points of the hill, for example. In quantum field theory things are similar. The vacuum energy is usually set to zero, and one can take all other energies relative to that one. However, this is not valid anymore if gravitation is taken into account. The value of the lowest energy cannot be set arbitrarily to zero because it may have an influence on space-time.
It means then that the energy level is an absolute level?

Is it theoretized that a residue inflationary field still active and not at the lowest possible minimum is still active, and could be the source for an accelerated expansion, as is assumed?

Is a true vacuum state the state with the absolute minumum of the potential, or the state with zero energy? I guess these do not have to coincide (hence, two different vacuum states)?

hellfire
In the standard model the scalar field responsible for inflation rolls down to the minimum of the potential. The true vacuum is defined to be the lowest energy level, the minimum, which must not be a zero energy level.

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Thanks hellfire,

This also means I guess that the vacuum state with zero energy density is not on the minimum of the potential, hence two different vacuum states?
(if I recall correctly, one is the "true" vacuum state, the other the "false" vacuum state?)

And yet another question (this inflationary theory got me curious), are negative potential field values allowed? Negative energy density?
(if I recall correctly the very reason for inflationary expansion is a negative pressure which acts as repulsive gravitation?)

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hellfire
The energy density is assumed to be positive and the negative pressure is given by an equation of state $p = - \rho$ during the slow-roll phase.