Undergrad Solving the Horizon Problem: 1 Source or 105?

[QuarkDecay]

TL;DR

Horizon problem in inflation and sources

It says that since there is homogeneity in the Universe's temperature, all these points must have come from one source (or a source close to each other?) at a certain time.
Then it also calculates the number of these sources and it's ~10⁵. But isn't that very dense mass right before the Big Bang considered to be just one source?
So is the Horizon problem the fact that we get 10⁵ different sources, while we should take only one? Or am I getting something wrong here?

 

[DaveC426913]

it also calculates the number of these sources and it's ~10^5

Source?
This is just a shot in the dark, but I found this reference to "10^5" associated with Inflation and the CMBR:

...the CMB is uniform (and therefore in thermal equilibrium) over the entire sky to one part in 10^5...

That's not what you're referring to is it?

 

[PeterDonis]

It says

What says? What are you referring to? You have provided no reference.

 

[QuarkDecay]

My notes from class say it. I didn't provide a source because this was the solution without the inflation correction, and also for the fact that this is not my main question.

 

[PeterDonis]

My notes from class say it.

We can't see your notes from class. So we don't know where all this about $10^5$ sources and so on is coming from. Please either give a reference to an actual source, like a textbook or peer-reviewed paper, or show us how this "number of sources" is calculated by posting the calculation directly in this thread.

this is not my main question.

We can't answer any of the questions you're asking without more information. See above.

 

[George Jones]

I think that the idea might be to calculate, assuming no inflation, the present angular size of a causally-connected region of the CMB, and then to calculate the number of these patches over the entire ($4 \pi$ solid angle) sky. In some sense, each of these patches should be treated as an independent source, since they can't (without inflation) communicate with each other.

I shouldn't be the one tracking sources (pun intended; groan), bu see equation (8.19) in

https://arxiv.org/abs/1803.00070
which is a draft version of a now published text.

 

[DaveC426913]

My notes from class say it. I didn't provide a source because this was the solution without the inflation correction, and also for the fact that this is not my main question.

You might want to check with your professor to correct your notes.

So is the Horizon problem the fact that we get 10^5 different sources, while we should take only one? Or am I getting something wrong here?

It certainly seems that way.

 

[Bandersnatch]

Then it also calculates the number of these sources and it's ~10^5. But isn't that very dense mass right before the Big Bang considered to be just one source?

No, because as you get further back in time towards the limit of the singularity, all points become causally separated. They never combine to form one source.

 

[timmdeeg]

So is the Horizon problem the fact that we get 10⁵ different sources, while we should take only one?

The temperature deviations in the CMB are so tiny that one should assume that the area which corresponds to our observable universe at the big bang was in thermal equilibrium. But this isn't possible because it turns out that only a very small patch of the CMB (roughly as small as the full moon) could have been in thermal equilibrium at the big bang recombination. It is this discrepancy which we call Horizon Problem.

 

[Bandersnatch]

But this isn't possible because it turns out that only a very small patch of the CMB (roughly as small as the full moon) could have been in thermal equilibrium at the big bang.

Not at the big bang, but at recombination.

 

[timmdeeg]

Not at the big bang, but at recombination.

Yes sure, thanks for correcting.

EDIT Now fixed.

 

[QuarkDecay]

The temperature deviations in the CMB are so tiny that one should assume that the area which corresponds to our observable universe at the big bang was in thermal equilibrium. But this isn't possible because it turns out that only a very small patch of the CMB (roughly as small as the full moon) could have been in thermal equilibrium at the big bang. It is this discrepancy which we call Horizon Problem.

This is what I was looking for. Not sure if I worded "sources" quite right. But it came from calculating the V⁰(trec)/V_H(trec)~1.4x10^5

 

[timmdeeg]

This is what I was looking for. Not sure if I worded "sources" quite right. But it came from calculating the V⁰(trec)/V_H(trec)~1.4x10^5

I've never heard about "sources" in this context but assume that the causally disconnected patches are meant.