Why is it surprising that the CMB is so homogeneous?

Question

I was reading the chat-room associated with this answer, and several times the point is made that the CMB being uniform breaks our expectation that it should be heterogeneous. The analogy given is that it would be weird if everyone showed up to a party dressed identically, and you would likely assume they had coordinated this. Other commenters point out that in other situations we wouldn't find it strange at all for everyone to be dressed identically; it wouldn't be a surprise to find everyone on a ship to be dressed like sailors. It seems to me both of these analogies miss the mark. A more similar analogy would be if you entered a random room at a convention hall; would you be surprised to find everyone dressed uniquely for a party, or identically for a sailor's convention?

Why would we have any expectations at all about the distribution of matter in the very early universe? I understand that the inflationary model is meant to bridge the gap between the heterogeneous early universe and the homogeneous CMB, but what if the universe was just homogeneous all along?

Answer 1

In both your examples you have to invoke some deus ex machina to ensure that (a) someone/something has recruited a load of people to be sailors and given them uniforms and (b) invited lots of people to a convention and instructed them on the dress code. For the analogy with the CMB to work there has to be no possibility that the sailors or convention attendees have coordinated with each other.

But that is the CMB homogeneity problem! Why would a bunch of people all turn up dressed the same if there appears to be no possibility that they could have communicated with each other? The solution is they received common instructions from some source that could communicate with all of them. In inflationary cosmology models, that source is an earlier epoch of inflation.

Answer 2

Why would we have any expectations at all about the distribution of matter in the very early universe?

You don't - but given that you have no expectations at all about how matter should be distributed, it should be surprising to see it's distributed uniformly. Like, if you have no expectations at all then presumably all the near-uncountable possibilities would be equally probable, and only a very small subset of them are uniform enough to produce the homogeneous CMB we see.

Consider: suppose I tell you I have a Rubik's cube on my desk. What is your credence that the Rubik's cube is in the solved state? The Rubik's cube has 43 quintillion states, so given no prior expectations, you should expect that all 43 quintillion states are equally probable. Most of them would look equally messy (to the human eye) and therefore are indistinguishable, but a select few will show some degree of order, and exactly one state shows perfect order (the one that's solved). Therefore, if I show you the cube and it's in the solved state, you should be surprised - or you should postulate that there's some process that leads to the cube becoming the solved state - which is what inflation is supposed to do.

Answer 3

Here's the thing about the uniformity of the CMB.

First we note that the specific energy spectrum of the radiation across wavelengths is a near-perfect example of a blackbody with a specific temperature. This spectrum is naturally created when radiation has had a chance to come into thermal equilibrium with hot matter. This very strongly suggests that all the parts and parcels of the universe were in close thermal contact with one another at very early times, long enough to smooth everything out to ~one part in 10,000.

The interesting problem is that we do not have an expansion mechanism or model in which 1) all parts of the universe "fireball" were in thermal contact with one another at early times and 2) yields the expanded universe we find ourselves inhabiting today. For cosmologists, this is a very big deal. Specifically, there wasn't any way in the classic big bang picture for all parts of the earliest universe to have had the opportunity to exchange heat and equilibrate.

Answer 4

This is basically an issue with all "fine tuning" type problems that show up in modern physics. There is nothing mathematically wrong with initial conditions where the matter density is initially uniform. And it is a defensible position to say that there's no sense in which one mathematically possible set of initially conditions is more or less likely than another set. To make a statement like that implies that one is using a probability distribution over the set of all possible initial conditions, and you could argue that this distribution is necessarily a subjective choice so you can't draw any rigorous, scientific conclusions drawn from it.

The perspective many physicists take, however, (including myself), is that parameters in physics should act as if they were drawn from some random distribution, modulo relationships that we know have to exist between parameters (like certain coupling constants having to be equal because of symmetries). An analogy in number theory is the heuristic random model of prime numbers -- it is widely believed that prime numbers should behave randomly up to patterns that are known to exist. So in that kind of picture, a perfectly homogenous initial condition is very surprising, because a typical draw from a reasonably broad distribution of initial conditions will not anything look like that.

To say it another way, we basically expect there shouldn't be patterns in the Universe unless we have an explanation for why that pattern is there. We don't have a reason to think that the initial conditions should be homogeneous, which would lead us to guess the initial density distribution should just be some arbitrary function, and therefore it's surprising when we find that distribution actually has a lot of structure. As far as we know, it could have been anything, so why did it turn out to be something so simple?

I'm painting a simple picture here, and you could push this discussion very far in lots of different directions -- you could challenge the model of the physical parameters we observe acting like they are drawn from a random distribution since we only ever see one world, you could ask precisely how you define a probability distribution over the parameters and how is such a distribution even defined in some cases, etc -- my point isn't to try to resolve any of those debates, just give some idea of where the intuition behind fine tuning problems comes from.

Answer 5

All of the answers here so far are resorting to two general explanatory strategies, but you’ve almost touched upon the crucial third explanatory strategy in your question – something constraining all the outfits to be the same. What might that something be?

So far, looking at the other answers, I only see two strategies mentioned. One is a “random explanation”, and from this perspective, the smoothness of the universe does look very surprising. The idea here is that given no other knowledge, all possibilities should be equally likely, so the best “explanation” is to draw a random one out of the mix. This is arguably no explanation at all, but it does work in certain cases – namely, as I see it, when there is nothing interesting to explain!

It's well known this sort of “random explanation” strategy in the early universe fails spectacularly, and not just for the smoothness problem. It also fails to explain the second law of thermodynamics, which needs a special initial boundary condition (a smooth one, as it turns out) for the “past hypothesis” that gives us observable arrows of time. (Given that all known microscopic physical laws are time-symmetric, we need an asymmetric initial condition to explain what we observe.)

The other sort of explanation offered so far has been the common idea of a “dynamical” explanation, to explain things in terms of earlier states. Unfortunately, in the case of the early universe, this just passes the explanatory buck to an earlier unexplained state. Maybe inflation can help solve the smoothness problem, but it still needs an extremely special starting point to explain the second law.

But it’s worth noting that there are other ways to make things uniform without having them interact with each other. The electric fields along a flat conductor are all pointing in the same direction. The small systems in contact with a large heat reservoir are all at the same temperature. These are examples of boundary constraints, and the most natural boundaries impose smoothness on the quantities which they constrain.

And that brings us to a third sort of explanation – a “boundary explanation”. Normally we don’t think of these sorts of explanations as fundamental – you can reduce my above two examples to dynamical explanations, after all. But there’s a special exception where boundary explanations might be more fundamental than the other two: at a cosmological boundary itself. If you run time all the way back to some literal initial boundary condition of the universe, then a dynamical explanation of that state has to fail, right? And, empirically, a random explanation does fail. (That’s the surprising smoothness of the universe you mention.) So why not look to boundary explanations here, why not posit that the initial boundary condition on the universe was smooth? In my experience physicists don’t tend to like this as an ultimate explanation, but in this case, I think it might be the right place to look.

Here's an essay I wrote about this once upon a time, with references.