A Closed Universe and the Horizon Problem

[jfy4]

Hi,

one of the problems that inflation right after the Big Bang solves is the horizon problem. While this post is not really related to inflation, I was wondering why a closed universe is not a more favorable candidate for the solution to that problem, rather than inflation.

Perhaps I have what the concept of a closed universe would look like wrong, but would a closed universe not a priori have a horizon, just like here on Earth were we can only see so far around the curvature of the planet. If the universe was closed, wouldn't this offer an already immediate answer to the horizon problem?

Thanks,

 

[Chalnoth]

Hi,

one of the problems that inflation right after the Big Bang solves is the horizon problem. While this post is not really related to inflation, I was wondering why a closed universe is not a more favorable candidate for the solution to that problem, rather than inflation.

Perhaps I have what the concept of a closed universe would look like wrong, but would a closed universe not a priori have a horizon, just like here on Earth were we can only see so far around the curvature of the planet. If the universe was closed, wouldn't this offer an already immediate answer to the horizon problem?

Thanks,

The horizon is the problem, in this case. If you take our universe and extrapolate back in time with the classical big bang theory, what you find is that widely-separated points have never been in causal contact. That is to say, if you look at the CMB, points separated by more than a couple of degrees or so on the sky have never been in causal contact. And yet, the entire CMB is uniform to one part in 100,000 in temperature. How did parts of the sky know to be the same temperature, when they've never been able to communicate?

That is the horizon problem. Inflation more or less solves this particular problem by proposing a different past expansion history that brings every point in the sky into causal contact during the inflationary epoch (inflation adds a new, similar problem, however).

 

[phinds]

Hi,

one of the problems that inflation right after the Big Bang solves is the horizon problem. While this post is not really related to inflation, I was wondering why a closed universe is not a more favorable candidate for the solution to that problem, rather than inflation.

Perhaps I have what the concept of a closed universe would look like wrong, but would a closed universe not a priori have a horizon, just like here on Earth were we can only see so far around the curvature of the planet. If the universe was closed, wouldn't this offer an already immediate answer to the horizon problem?

Thanks,

Quite possibly just due to ignorance on my part, I don't understand what the horizon problem has to do with whether or not the U is open or closed. If the U is open, it just goes on forever and you have the horizon problem. If the U is closed, it just LOOKS like it goes on forever but curls back on itself in some way we 3D creatures can't get our brains around (well, I can't anyway) but you STILL have the horizon problem.

Am I missing something?

 

[jfy4]

Quite possibly just due to ignorance on my part, I don't understand what the horizon problem has to do with whether or not the U is open or closed. If the U is open, it just goes on forever and you have the horizon problem. If the U is closed, it just LOOKS like it goes on forever but curls back on itself in some way we 3D creatures can't get our brains around (well, I can't anyway) but you STILL have the horizon problem.

Am I missing something?

No most likely I am missing something. This is my understanding. Humans had a horizon problem with Earth. It looked like it just stopped and who knew what was beyond. But there was no horizon, in the sense we thought back then. The Earth is curved and the horizon is not an end of the Earth or anything special, just a curved surface. I thought with a closed, spherical, in some sense of the word, universe, that it would also explain the "horizon". That it is not an end or anything like that, just like it was not the end of the earth. Does that clarify what I was thinking?

 

[phinds]

No most likely I am missing something. This is my understanding. Humans had a horizon problem with Earth. It looked like it just stopped and who knew what was beyond. But there was no horizon, in the sense we thought back then. The Earth is curved and the horizon is not an end of the Earth or anything special, just a curved surface. I thought with a closed, spherical, in some sense of the word, universe, that it would also explain the "horizon". That it is not an end or anything like that, just like it was not the end of the earth. Does that clarify what I was thinking?

AH ... I see completely what you were talking about. What you are partly missing is that the "horizon problem" is a standard cosmological puzzle which has to do with the CMB and which is solved by massive inflation in the early universe, as you stated. chalnoth's post explains it well. Based on your post, I think you pretty much have this. It's the fact that inflation sovles the horizon problem and some others that make it (inflation) so widely accepted.

Open and closed U's don't affect the horizon problem since the "edge" of our OU is not affected by whether the U is open or closed. Well, I guess maybe it COULD be affected if space were not so flat but I don't know enough to be sure about that.

 

[Chalnoth]

Open and closed U's don't affect the horizon problem since the "edge" of our OU is not affected by whether the U is open or closed. Well, I guess maybe it COULD be affected if space were not so flat but I don't know enough to be sure about that.

Well, the details of the horizon are down to the expansion history of the universe, both past and future. How the universe has expanded in the past says how much we are able to see today. How the universe expands into the future says how much we will ever be able to see.

And since the overall spatial curvature does have some impact upon the expansion history, it does impact how much we can see. However, since the discovery of the accelerated expansion, it seems that most likely, the dark energy will have vastly more to say about the future expansion than curvature. We also know that the curvature had to have no more than a small effect on the past expansion because we haven't yet had any definitive measurements of deviation from flat space despite massive advancements in measurement accuracy.

 

[phinds]

Well, the details of the horizon are down to the expansion history of the universe, both past and future. How the universe has expanded in the past says how much we are able to see today. How the universe expands into the future says how much we will ever be able to see.

And since the overall spatial curvature does have some impact upon the expansion history, it does impact how much we can see. However, since the discovery of the accelerated expansion, it seems that most likely, the dark energy will have vastly more to say about the future expansion than curvature. We also know that the curvature had to have no more than a small effect on the past expansion because we haven't yet had any definitive measurements of deviation from flat space despite massive advancements in measurement accuracy.

Am I correct in believing that IF the U were not so flat, then the curvature of space WOULD have had more of an effect. I think that's what you're saying in "And since the overall spatial curvature does have some impact upon the expansion history", just want to be sure.

Thanks

 

[Imax]

While this post is not really related to inflation, I was wondering why a closed universe is not a more favorable candidate for the solution to that problem, rather than inflation.

A closed universe does not exclude inflation. The universe can form a closed manifold and that manifold can increase in size with time.

 

[Chalnoth]

Am I correct in believing that IF the U were not so flat, then the curvature of space WOULD have had more of an effect. I think that's what you're saying in "And since the overall spatial curvature does have some impact upon the expansion history", just want to be sure.

Thanks

Well, yes, but not an overly-dramatic one. Basically, the curvature is constrained to be quite flat by our very existence: too much curvature, and the universe recollapses too rapidly for anything to form. Too little, and it expands to rapidly for any structures to form. So you can't actually change the horizon by very much by changing the curvature, as long as you still want a habitable universe.

Now, if there were no dark energy, or the dark energy somehow decayed in the future, then it is actually the curvature that becomes the dominant factor determining the future of our universe.

 

[phinds]

Well, yes, but not an overly-dramatic one. Basically, the curvature is constrained to be quite flat by our very existence: too much curvature, and the universe recollapses too rapidly for anything to form. Too little, and it expands to rapidly for any structures to form. So you can't actually change the horizon by very much by changing the curvature, as long as you still want a habitable universe.

Now, if there were no dark energy, or the dark energy somehow decayed in the future, then it is actually the curvature that becomes the dominant factor determining the future of our universe.

Interesting, thanks. No, I didn't mean at all to constrain it to a habitable U, I'm more interested in space/time and we have no effect on that anyway (although I do understand that it has an effect on our existence, as you said).