Creation and Destruction of Imaginary Particles in A vacuum and Relation to Size of Universe

[CuriousOnes]

We know that elementary particle anti-particle pairs appear and annihilate even in a vacuum.  This phenomena is (I believe) happening everywhere in the Universe, vacuum or not.

What struct me as an interesting question and brought me here is whether the (volume?/quantity?/energy density?) of this phenomena is influenced by the expansion of the universe.  For Example, say the rate of particle anti-particle pair creation is 100MUU (Made Up Units) per M^3, would that value decrease over time as the Universe expands.  Or more interestingly, have been twice as prevalent when the universe was half its present size?  Nearly infinitely more powerful right after the big bang?

If I'm even close to being grounded with this question, the follow up question is whether this is a remotely testable theory.

[Genady]

6 minutes ago, CuriousOnes said:

We know that elementary particle anti-particle pairs appear and annihilate even in a vacuum.  This phenomena is (I believe) happening everywhere in the Universe, vacuum or not.

What struct me as an interesting question and brought me here is whether the (volume?/quantity?/energy density?) of this phenomena is influenced by the expansion of the universe.  For Example, say the rate of particle anti-particle pair creation is 100MUU (Made Up Units) per M^3, would that value decrease over time as the Universe expands.  Or more interestingly, have been twice as prevalent when the universe was half its present size?  Nearly infinitely more powerful right after the big bang?

If I'm even close to being grounded with this question, the follow up question is whether this is a remotely testable theory.

Let me try. As the universe expands it gets more vacuum. But it is the same vacuum, the vacuum does not dilute. Thus, the answer to the questions is, No.

[swansont]

36 minutes ago, Genady said:

Let me try. As the universe expands it gets more vacuum. But it is the same vacuum, the vacuum does not dilute. Thus, the answer to the questions is, No.

If the universe had a finite size, wouldn't the mode density of the vacuum energy levels change with the volume?

[Genady]

18 minutes ago, swansont said:

If the universe had a finite size, wouldn't the mode density of the vacuum energy levels change with the volume?

On a smaller scale, perhaps it would. But if this finite size of the universe is greater then the size of event horizon, I don't know how expansion behind event horizon affects the energy levels here. Do you?

[swansont]

10 minutes ago, Genady said:

On a smaller scale, perhaps it would. But if this finite size of the universe is greater then the size of event horizon, I don't know how expansion behind event horizon affects the energy levels here. Do you?

What event horizon?

[Genady]

4 minutes ago, swansont said:

What event horizon?

Cosmological event horizon.

[swansont]

No, I don't know.

Can you have a mode that's got a wavelength longer than 2x of the event horizon? I don't know what boundary conditions apply.

[Genady]

1 hour ago, swansont said:

No, I don't know.

Can you have a mode that's got a wavelength longer than 2x of the event horizon? I don't know what boundary conditions apply.

Yep, this is my question, too.

[MigL]

In the case of inflation, it is the 'roll' from the false zero energy of the vacuum to the real ( ? ) zero level due to a symmetry break, where vacuum energy is traded for exponential inflation.
If that is also the case for expansion, then vacuum energy would be similarly decreasing.
And if we consider the Mexican hat  potential, then even periods of accelerated expansion could be exlained in terms of oscillations about the real zero level.

[Genady]

17 minutes ago, MigL said:

In the case of inflation, it is the 'roll' from the false zero energy of the vacuum to the real ( ? ) zero level due to a symmetry break, where vacuum energy is traded for exponential inflation.
If that is also the case for expansion, then vacuum energy would be similarly decreasing.
And if we consider the Mexican hat  potential, then even periods of accelerated expansion could be exlained in terms of oscillations about the real zero level.

How it is if we restrict the question to one regime, after inflation and before the expansion accelerated again, i.e. say between 3 s and 7 billion years or so after BB, when the expansion was decelerating due to the matter and radiation content?

4 hours ago, CuriousOnes said:

We know that elementary particle anti-particle pairs appear and annihilate even in a vacuum. ...  have been twice as prevalent when the universe was half its present size?  Nearly infinitely more powerful right after the big bang?

 

I think the OP meant virtual rather than imaginary particles. My answer to the OP questions stays. No.

Edited January 20, 2022 by Genady

[MarcoBarbieri]

On 1/20/2022 at 9:48 PM, MigL said:

And if we consider the Mexican hat  potential, then even periods of accelerated expansion could be exlained in terms of oscillations about the real zero level.

How can a field, the Higgs field, have a central maximum (the top of the hat) in energy when the field is zero? Aren't we, by this artificially constructed image, led to the conclusion that the Higgs mechanism is an imaginary mechanism only? With no real existence?

[Genady]

16 minutes ago, MarcoBarbieri said:

How can a field, the Higgs field, have a central maximum (the top of the hat) in energy when the field is zero? Aren't we, by this artificially constructed image, led to the conclusion that the Higgs mechanism is an imaginary mechanism only? With no real existence?

Take a spring. Let's call it's length = total length - sum of widths of the coils. When it squeezed maximally, its length is zero. It has non-zero energy there. When it relaxes it expands, so the minimum energy is at the length greater than zero. This spring has a very real existence  

[MigL]

It is vacuum energy, which drops after the Big Bang event as the universe evolves.
It has symmetries which we no longer see, and at some point it reaches a low but unstable energy. Then a symmetry break enables the break up of the Electroweak force via  the Higgs mechanism, and its associated field results in mass for its bosons ( and all leptons )
I like to picture a pencil dropped from a height, that lands on its tip; low energy, but symmetric ( rotation ) and unstable.
At some point, symmetry is broken and the pencil falls over.
No longer symmetric, with a specific direction, but at even lower, or true, minimum energy.