Understanding Horizon Distance in Axion Cosmology Model

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In summary, the conversation discusses the concept of domain walls and their formation in the context of axion cosmology. The paper being referenced explores the idea that after the PQ symmetry is broken, the flat direction in the mexican hat potential becomes sharp points, creating strings between them. When the axion mass is turned on, each string becomes the edge of N domain walls. The conversation also discusses the idea that there can be multiple degenerate vacua, leading to the formation of multiple domain walls. The conversation concludes by discussing the differences between domain walls in cosmology and in magnetic moments.
  • #1

ChrisVer

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I am having some problems with understanding what it means to be in the horizon of something else. In particular I'm looking into axion cosmology model.
In this paper, and in particular in the strings and wall decay sections:
http://arxiv.org/abs/astro-ph/0610440
Let me try to elaborate some of the ideas. When PQ symmetry is broken and after QCD phase transition it gets broken: [itex]U(1) \rightarrow Z(N)[/itex], I think that this means that in the mexican hat potential, the flat direction becomes like this:
/\/\/\/\/\/\/\/\
with N sharp points. Between these points there are created the strings, correct?
If not, what does he mean by:
When the axion mass turns on, at time t1, each axion string becomes the edge of N domain walls
?

Also in the same paragraph he takes [itex]N \ge 2[/itex] so at least the flat direction gets at least two spikes along its way (/\/\):
Since there are two or more exactly degenerate vacua and they have identical properties, the vacua
chosen at points outside each other’s causal horizon are independent of one another. Hence there is at least on the order of one domain wall per causal horizon at any given time.
So I am wondering, why is that "hence" true? the domain wall appears in the field's configuration space, and not in the general spacetime...any help?
 
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  • #2
ChrisVer said:
So I am wondering, why is that "hence" true? the domain wall appears in the field's configuration space, and not in the general spacetime...any help?
I think it helps to visualize how these phase transitions occur, and why domain walls form. They don't occur instantaneously: you get a nucleation in one specific location that spreads. All phase transitions work this way. So a specific domain starts when one tiny region of space-time settles into the new semi-stable vacuum state, and that specific state is random. This new vacuum state then spreads outward at nearly the speed of light, until it collides with another vacuum state where it isn't energetically favorable to continue spreading.

This is where the horizon comes in: even at the speed of light, the vacuum state cannot spread beyond the future horizon of that original nucleation. So you're guaranteed a domain wall somewhere within its future horizon (because eventually another nucleation will occur close enough to collide with this one).
 
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  • #3
So suppose I get two points, causally non-connected, A and B.
In A,B I will have this breaking (transition) and so let's take the case [itex]N=2[/itex] there will be created two vacua (1 /\ 2/\)... So let's say that A settles in 1 (randomly).
This will start spreading with the speed of light. If B also settles in 1, then they will both be in the same vacuum once they get causally connected. If it settles in 2 I will have two different vacua "colliding" and so 1 wall between them...
Is that interpretation correct?
 
  • #4
ChrisVer said:
So suppose I get two points, causally non-connected, A and B.
In A,B I will have this breaking (transition) and so let's take the case [itex]N=2[/itex] there will be created two vacua (1 /\ 2/\)... So let's say that A settles in 1 (randomly).
This will start spreading with the speed of light. If B also settles in 1, then they will both be in the same vacuum once they get causally connected. If it settles in 2 I will have two different vacua "colliding" and so 1 wall between them...
Is that interpretation correct?
Yes. But the expectation is that the number of possible vacuum states is quite vast (infinite in some models), so it's highly unlikely for two causally-disconnected points to fall into the same vacuum state.
 
  • #5
true, but then you shouldn't expect of the order of one domain walls per horizon, but it should be like ...
Taking eg [itex]N=3[/itex] (3 degenerate vacua), we can choose 3 points in the same logic, that fall in vacuum 1, 2 and 3.
Where they meet each other, you will have 3 walls (1-2 , 2-3, and 1-3).
And doing the same for a general N , and N distinct points, you get way more walls.
 
  • #6
ChrisVer said:
true, but then you shouldn't expect of the order of one domain walls per horizon, but it should be like ...
Taking eg [itex]N=3[/itex] (3 degenerate vacua), we can choose 3 points in the same logic, that fall in vacuum 1, 2 and 3.
Where they meet each other, you will have 3 walls (1-2 , 2-3, and 1-3).
And doing the same for a general N , and N distinct points, you get way more walls.
It depends a bit upon the model. If a stable domain wall is rare, then you generally won't get more than one domain wall. For example, if a domain wall will always spread in the direction of the lower-energy vacuum state at nearly the speed of light, and vacuum states with the same energy don't exist (or are very rare), then every domain will rapidly expand to encompass its entire horizon, or else be overcome by a different domain with lower vacuum energy.

But either way, it's easy enough to take N=1 as a reasonable lower-bound on the expected frequency of domain walls.
 
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  • #8
ChrisVer said:
Are the domain walls in this case different to the ones you get in the magnetic moments examples?
http://en.wikipedia.org/wiki/Domain_wall_(magnetism)
Because then I don't understand the "stability" or "spreading"...
The main difference there is that each domain has equal energy, so that domain walls collide but remain stationary. Think of it more like the domain walls between liquid and gas in a vat of boiling water.
 
  • #9
doesn't degenerate vacua have the same energy?
 
  • #10
Certainly, by definition. Why would the different domains be degenerate?
 
  • #11
Hmmm... it sounds logical to me... because all points within the domain will fall in the same vacuum.
If all points of domain 1 are in vacuum 1, and all points of domain 2 are in vacuum 2, but vacuum1=vacuum2 (coming from Z(N) SSB), then also the domains should be degenerate.
I think I am missing something important or doing something wrong...
 
  • #12
ChrisVer said:
Hmmm... it sounds logical to me... because all points within the domain will fall in the same vacuum.
If all points of domain 1 are in vacuum 1, and all points of domain 2 are in vacuum 2, but vacuum1=vacuum2 (coming from Z(N) SSB), then also the domains should be degenerate.
I think I am missing something important or doing something wrong...
Looked into the specific model they're using in a bit more detail, and they're saying that while the domains have identical energies, the domain walls repel one another gravitationally. This repulsion is likely what gives rise to the ~1 domain wall per horizon: as long as the repulsion is large enough compared to the decay rate, so that the wall expands to fill its horizon before there's a chance for another domain to form, then you'll only get approximately one domain wall per horizon on average.
 

1. What is horizon distance in axion cosmology model?

Horizon distance in axion cosmology model refers to the maximum distance that light can travel before the end of inflation. It marks the boundary of observable universe and is an important parameter in understanding the evolution of the universe.

2. How is horizon distance calculated in axion cosmology model?

Horizon distance in axion cosmology model is calculated using the Hubble constant, which is a measure of the expansion rate of the universe. It can also be calculated using the age of the universe and the speed of light.

3. What is the significance of horizon distance in axion cosmology model?

Horizon distance in axion cosmology model plays a crucial role in determining the size and age of the observable universe. It also provides insights into the early stages of the universe, such as the inflationary period and the formation of large-scale structures.

4. How does the axion field affect horizon distance in the cosmology model?

The axion field can significantly affect the horizon distance in the cosmology model by altering the expansion rate of the universe. This, in turn, can affect the size and age of the observable universe and the evolution of large-scale structures.

5. Can horizon distance in axion cosmology model be observed or measured?

No, horizon distance in axion cosmology model cannot be directly observed or measured as it marks the boundary of the observable universe. However, it can be inferred from other cosmological parameters and observational data.

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