Question on the horizon problem

• I
Nikolai01
Hi Physics Forums,

I had a question on the horizon problem (explanation for apparent thermal equilibrium between distal points on the CMB, anisotropies notwithstanding). Just as background, I just have an amateur interest in cosmology with no formal training (biophysist by training and career), so please forgive and inform if I'm totally off-base somewhere.

Prior to my actual question on the horizon, I have a preliminary question on the nature of the initial singularity post-big bang. As I understand it, although the current universe appears spatially flat inflation could have minimized any curvature present, and driven the universe to apparent flatness. Thus the early universe could have been significantly curved.

Going back in time, what would be the nature of space as we approach the initial singularity in the three different curvature regimes? Intuitively, for a closed universe I can envision everything collapsing towards a single point (perhaps with non-trivial topology) as t-->0; a closed bounded universe space then just expands in all directions from all points.

For flat or open universes, however, what would be the nature of the initial singularity? Both of those universes, as I understand it, are infinite in scale. No matter how many fold you shrink infinity, it'll still be infinity, so as t-->0 in those universes does the initial singularity which it approaches still have infinite scope/volume in our 3d space?

I'll hop back on with my actual horizon question once I get some feedback on the above, as the questions are intertwined. ;-D

Homework Helper
Gold Member
2022 Award
Going back in time, what would be the nature of space as we approach the initial singularity in the three different curvature regimes? Intuitively, for a closed universe I can envision everything collapsing towards a single point (perhaps with non-trivial topology) as t-->0; a closed bounded universe space then just expands in all directions from all points.

For flat or open universes, however, what would be the nature of the initial singularity? Both of those universes, as I understand it, are infinite in scale. No matter how many fold you shrink infinity, it'll still be infinity, so as t-->0 in those universes does the initial singularity which it approaches still have infinite scope/volume in our 3d space?

Yes, a spatially infinite universe remains infinite no matter how dense it becomes.

Singularity means a breakdown in the mathematical model and not a single point. If you go back far enough, the energy density of the early universe goes beyond where we have confidence in the mathematical models. Some new physics is needed at this stage.

Nikolai01
Yes, a spatially infinite universe remains infinite no matter how dense it becomes.

Singularity means a breakdown in the mathematical model and not a single point. If you go back far enough, the energy density of the early universe goes beyond where we have confidence in the mathematical models. Some new physics is needed at this stage.

Great, thanks. Always good to remember it as a mathematical singularity, it's to easy to just fall into the trap of imaging the big bang as just an uber-point black hole running in reverse.

I had two thoughts/questions about the necessity of inflation to help solve the horizon problem. The problem, as I've heard it formulated, is that the CMB is at the same temperature (barring small anisotropies) at all points even though most points on the CMB were too far apart to have been able to interact and acquire thermal equilibrium before decoupling. How would points in space that have never interacted attained thermal equilibrium? Inflation solves this issue by starting with a small volume in the early universe that is allowed to attain thermal equilibrium, then inflating it so that patch is larger than the current observable universe.

I had been bouncing around two ideas (perhaps related) which would allow temperature homogeneity even in points too far apart to directly equilibrate. I'm curious if these are ideas that have been discussed and/or if there are some glaring flaws in the ideas.

Question A: Simultaneity of big bang at distal points

An open or flat universe remains infinite as t-->0 towards the big bang, thus assuming it had a "start" (and time doesn't continue back to negative infinity). Do points in the universe that are far apart "start" or emerge from the singularity state at the same time?

Now, I know the question of simultaneity is vague due to relativity (which I'm not at all strong in), and that would be compounded even more by the singularity. However, if times were not synched up it seems like there would be a couple glaring issues. First, it seems like that would violate homogeneity if two interacting parts of the universe had had different amounts of time to evolve (though I don't know if homogeneity is a hard-and-fast principle). Second, if one part of the universe were "older" and one part were "younger" it seems like it would create a big innate dipole in the CMB, as one half of the universe would have cooled and recombined sooner and thus suffered more of a redshift due to expansion. (though I suppose if inflation occurred it could wipe this out).

Writing it down I realize my arguments are perhaps not so clearly stated, I don't necessarily have the theoretical chops. Trying to simplify the question: did the points of space which emitted CMB light from opposite points in the sky come into being at the same time (or at least appear to from our perspective)? If they did not, then I would expect there to be large-scale gradients of temperature across the sky (there isn't). If they did come into being at the same time, then it would seem to violate speed-of-light causality: they are points that are distal from each other which came into being at exactly the same time. If different points in space were able to "communicate" in the sense that they were able to come into being at the same time despite being light-years apart (as many points would be in a spatially infinite universe), why is it not possible for them to "communicate" temperature as well, and come into existence at the same temperature without having to explicitly thermalize?

Is the answer to this question that there is some vagueness about simultaneity of the formation of the universe early on? Things happen more-or-less simultaneously because everything is entangled in the super-hot early universe?

Question B: The melting temperature hypothesis

Translating the experiment into a biochemistry lab (where I have more experience), imagine you've got two beakers of equilibrated ice water at opposite ends of your 20°C lab. Those two little universes are not thermally interacting, and there is no active feedback or communication between them, yet they are both at exactly the same temperature: 0°C.

Would the universe have emerged from the singularity via a similar phase transition, a constant "melting temperature"? When the universe emerges from the singularity, it comes out at a set temperature defined by the various constants of our universe. Thus, different parts of an infinite cosmos would have started at the same temperature, even though they've never been able to thermalize or communicate. Thus, CMB photons reaching us from opposite sides of the universe would be the same temperature, even if those regions had never been able to directly interact or communicate.

These two questions struck me as ways in which we could have gotten the nearly isotropic CMB background temperature without the need for inflation. Clearly, these ideas don't help with forming the CMB anisotropies. Thank you for reading my novel of a post--these are just some thoughts that have been bouncing around my head for a while, I would love to get some feedback or insight on them.

Last edited:
Homework Helper
Gold Member
2022 Award
You might need one of the cosmology experts to answer your questions. All I have is this lecture by Alan Guth, in case you haven't seen it:

Mentor
I had been bouncing around two ideas (perhaps related) which would allow temperature homogeneity even in points too far apart to directly equilibrate.
Personal speculations are off limits for discussion here. You need to learn what our best current theories actually say, not try to guess.

Do points in the universe that are far apart "start" or emerge from the singularity state at the same time?
You're looking at it backwards. The emergence of comoving observers from the singularity defines "at the same time". So your question can't even be posed; it's true by definition.

Would the universe have emerged from the singularity via a similar phase transition, a constant "melting temperature"
No. The singularity is not a boundary between different phases. As @PeroK has said, it's a regime in which our current theories break down. That means it's meaningless to ask what our current theories predict about what comes out of a singularity; they can't predict anything, because they break down there.

2022 Award
If they did come into being at the same time, then it would seem to violate speed-of-light causality: they are points that are distal from each other which came into being at exactly the same time. If different points in space were able to "communicate" in the sense that they were able to come into being at the same time despite being light-years apart (as many points would be in a spatially infinite universe), why is it not possible for them to "communicate" temperature as well, and come into existence at the same temperature without having to explicitly thermalize?
I think this is a reasonable question, despite the prohibition on speculation.

That everything apparently emerged from the Big Bang singularity at the same time is (in the model) a consequence of the cosmological principle, that everything is the same everywhere. Necessarily, then, everything emerged from the singularity at the same time (in that sense of time) because anything else would violate the cosmological principle. So asking why it happened comes down to asking "why the cosmological principle". But you cannot find the answer in the singularity: that's literally the maths telling you that the theory doesn't work there. You need a different theory.

There isn't a causal problem with distances inside the universe growing faster than light, by the way. A better statement of the light speed limit is that nothing will ever overtake a light ray in a race, and nothing ever does, even as distances grow arbitrarily rapidly.

PeroK
Nikolai01
Personal speculations are off limits for discussion here. You need to learn what our best current theories actually say, not try to guess.
I agree, which is why I wanted to bounce my thoughts off of others who have discussed the field in more depth and get feedback. ;-)

You're looking at it backwards. The emergence of comoving observers from the singularity defines "at the same time". So your question can't even be posed; it's true by definition.

No. The singularity is not a boundary between different phases. As @PeroK has said, it's a regime in which our current theories break down. That means it's meaningless to ask what our current theories predict about what comes out of a singularity; they can't predict anything, because they break down there.
Got it...I've been working mostly off Liddle's Intro to Modern Cosmology. When he presented the horizon problem, I read it as being a 2-fold problem: 1) How points of space too far apart to interact before decoupling could be at the same temperature, and 2) How irregularities/anisotropies would be introduced in the background. Because he had brought up problem 1 I had come from the perspective that there was some assumption within the field that they wouldn't start at the same temperature, but I'm reading from your statement that that isn't necessarily the case. Am I reading your statement correctly in that we cannot predict whether the universe would have come out of the singularity at the same temperature at all places, so that either:

1) The universe started at the same temperature everywhere, so inflation is not required to explane the relative isotropy of the CMB (though it obviously helps explain the anisotropies).
or
2) The universe did not start at the same temperature everywhere, but inflation (or some other effect) expanded that inhomogeneity beyond our horizion, and also added the anisotropies.

And we are not currently in a position to determine which of those two is the case? That was the crux of much of what I was wondering, whether the universe could have been thermally homogeneous at extremely early times, and it sounds like the answer is "Maybe, because we can't predict what comes out of a singularity."

And so the end answer is that we're not sure whether inflation was required to explain the relative isotropy of the CMB, because we cannot know what emerged from the singularity? We thus can't use the relative overall isotropy of the CMB as necessary proof for the idea of inflation (although inflation does give an additional reason why it would be isotropic). Rather, it is the anisotropies and the science and modeling associated with them that supports the idea of inflation?

Last edited:
Nikolai01
I think this is a reasonable question, despite the prohibition on speculation.

That everything apparently emerged from the Big Bang singularity at the same time is (in the model) a consequence of the cosmological principle, that everything is the same everywhere. Necessarily, then, everything emerged from the singularity at the same time (in that sense of time) because anything else would violate the cosmological principle. So asking why it happened comes down to asking "why the cosmological principle". But you cannot find the answer in the singularity: that's literally the maths telling you that the theory doesn't work there. You need a different theory.

There isn't a causal problem with distances inside the universe growing faster than light, by the way. A better statement of the light speed limit is that nothing will ever overtake a light ray in a race, and nothing ever does, even as distances grow arbitrarily rapidly.
Yeah, what I was struggling with is how two different points light-years apart could get the "go" signal at the absolutely same time (at least from the perspective of our observation point) . Granted, that is a perspective of movement and a speed that is forbidden within the universe while this issue is with the start of the universe and emergence of the singularity, which is not necessarialy bound by the same rules. And as you and the previous poster say the math's don't work there, and we can't really predict.

Mentor
I agree, which is why I wanted to bounce my thoughts off of others who have discussed the field in more depth and get feedback. ;-)
"Bouncing your thoughts off of others" is personal speculation. And it's off limits here.

I've been working mostly off Liddle's Intro to Modern Cosmology.
That's a good reference to use.

Mentor
When he presented the horizon problem, I read it as being a 2-fold problem: 1) How points of space too far apart to interact before decoupling could be at the same temperature, and 2) How irregularities/anisotropies would be introduced in the background.
Some specific references to the textbook here would be helpful. The horizon problem is usually considered to be 1), which is what inflation models claim to solve. I have not seen 2) brought up in the context of the horizon problem.

Mentor
what I was struggling with is how two different points light-years apart could get the "go" signal at the absolutely same time
Where do you see this in Liddle's textbook? Please give specific references.

The reason I'm belaboring this is that before you can even use a model to frame questions, you have to understand what it says and what it doesn't say. It's not enough to read a few things about it and then go off on your own. You need to thoroughly understand the model, including its math.

Mentor
we cannot predict whether the universe would have come out of the singularity
That statement is correct as a statement about General Relativity. Notice that I omitted the qualifier you put in; the statement is correct without any qualifiers at all.

However, you are drawing the wrong conclusion from it. You are drawing the conclusion that we have to somehow come up with an independent assumption about "how the universe started", and then work forwards from that. That's wrong.

The correct conclusion is that we cannot construct a model of how the universe started at all by working forward with our current theories. We will only be able to do that working forward if we come up with a more comprehensive theory, such as a theory of quantum gravity, that replaces GR in the regime in question and makes definite predictions.

In the meantime, the only thing cosmologists can do is to work backwards. We take the earliest state of the universe for which we have good evidence, namely, the hot, dense, rapidly expanding state that, in inflation models, occurs at the end of inflation, and try to figure out what could have preceded it. The goal is to work as far backwards as we can without running into the regime where our theories break down.

PeroK
Mentor
That was the crux of much of what I was wondering, whether the universe could have been thermally homogeneous at extremely early times, and it sounds like the answer is "Maybe, because we can't predict what comes out of a singularity."
No, the answer is "we have no way of making any prediction about this at all by working forwards". See post #12. That doesn't mean we can just make things up. It means we have no basis for even speculating as far as working forwards is concerned. All we can do is work backwards as I described in post #12.

Staff Emeritus
I had a professor once pass back an exam (all essay questions) saying "You will notice that at no time did I ask you what you think. I don't care what you think. I want to know if you know what Emile Durkheim thought."

Conn_coord
I had a professor once pass back an exam (all essay questions) saying "You will notice that at no time did I ask you what you think. I don't care what you think. I want to know if you know what Emile Durkheim thought."
A good teacher should teach thinking rather than learning by heart. Without new ideas, science degenerates. And new ideas will not appear in old textbooks, no matter how luminaries of science they would not be written.

andrew s 1905 and weirdoguy
2022 Award
And new ideas will not appear in old textbooks, no matter how luminaries of science they would not be written.
But you will not generate new ideas if you don't already understand existing knowledge. You don't have time in your life to re-derive everything from scratch. You need to know what we already know so you understand what the problems are, and you need to be able to separate that knowledge from your own analysis of it.

So sure, thinking is needed, but you can't think about what you don't know.

Hornbein and PeterDonis
Conn_coord
So sure, thinking is needed, but you can't think about what you don't know.
Agree that there are extremes. Or you do not understand the topic at all and your ideas are rubbish. Or you are so carried away by the study of different points of view that you become a slave to this process and you do not have time for your interpretation.

Gold Member
Agree that there are extremes. Or you do not understand the topic at all and your ideas are rubbish. Or you are so carried away by the study of different points of view that you become a slave to this process and you do not have time for your interpretation.
A pf poster summed it up, "before trying to think outside the box, learn what is in the box."

Phinds I think.