# How is the Cosmic Microwave Background so big?

If the CMB is an image of the universe when it was 379,000 years old, how is it so large? Since the light is 13.8 billion years old, the image represents the surface of a sphere with a radius of 13.8 billion light years, and I don't think the universe would have been that large at that age. Even if it was, an image from further back in time would be larger, which doesn't make any sense, since the universe expands.

• To clarify, when I say CMB here, I refer to the image of it, not the radiation itself. Commented Sep 24, 2023 at 9:58
• “Even if it was, an image from further back in time would be larger, which doesn't make any sense, since the universe expands.” Actually, you are correct, As you go further back in time and distance, objects will appear larger, because the universe expands. Commented Sep 24, 2023 at 16:00
• The universe is probably infinite, and if so, it was always infinite. See physics.stackexchange.com/q/136860/123208 & astronomy.stackexchange.com/a/31795/16685 Commented Sep 24, 2023 at 17:29
• When you don't think the universe would have been that large at that age, how big do you think it should have been? Commented Sep 25, 2023 at 19:38
• I'm no physicist, but I've read a bunch of books about physics, cosmology, etc. Can someone who is an expert on this possibly write up an answer based on (or at least including) inflation? Commented Sep 26, 2023 at 21:38

The CMB isn't really an image of the universe. The universe is full of the CMB radiation, with (almost) equal numbers of photons travelling in all directions at every point in space. An analogy would be taking a picture of fog from within the fog.

We are immersed within the cosmic microwave radiation field and our position (and every other position) in the universe has always been fully immersed in this radiation field.

All those photons have indeed been travelling from elsewhere in the universe since they were created 13.8 billion years ago. The regions from which those photons originate are now, thanks to the expansion of the universe, about 46 billion light years away. The uniformity of the cosmic microwave background tells us that the universe is very homogeneous on scales at least as large as this.

i.e. The CMB photons we see now come from a sphere around us that is now (at this cosmic epoch) 46 billion years in radius. In a billion years time they will come from a sphere around us that is correspondingly larger.

• Firstly, I'm not asking about the origin of those photons now, I'm asking about the origin of those photons back then. Secondly, every source I've ever seen or heard has said that the CMB image is a 360-degree microwave image from 13.8 billion years ago, which I understand would mean it is an image of the universe back then, just of microwaves instead of visible light. (Edited because I thought Enter would make a new line, not Shift-Enter) Commented Sep 24, 2023 at 9:49
• @ProximaAce The CMB isn’t an image in the traditional sense. Some of its structures are created by the physics pertaining to the matter where the light was first emitted (when the primordial plasma became transparent), whereas some of the structures pertain to the physics of matter it encountered soon after emission, and some pertain to matter it encountered billions of years later (e.g the Sunyaev-Zeldovich effect). Combine that with it being omni-directional, and our intuition about interpreting features of images is not very helpful. Commented Sep 25, 2023 at 2:09
• @ProximaAce So to summarize, people say the CMB is an image of the early universe because most of its most obvious features do pertain to that epoch, but it isn’t really a straightforward “picture” of how the early universe “looked”. For example, the correspondence of hot spots/cold spots and overdensities/underdensities is reversed depending on whether you are looking at large scale hotspots/coldspots or small scale ones. There’s not really equivalent phenomena in traditional optics outside of maybe some kind of optical illusion. Commented Sep 25, 2023 at 2:15

The size of the CMB sphere is not related to the size of the universe. It could be that the universe is infinite in size, and was infinite in size when the CMB was emitted. It could also be that the universe is smaller than the CMB sphere; that's just another way of saying that CMB light could have circumnavigated the universe at least once between emission and detection. I think the latter is ruled out experimentally, but it's possible in theory.

I think it's reasonable to say that the CMB is an image, but it's not an image of the whole universe, just a spherical slice of it. The universe isn't (and wasn't) spherical in shape. If the spatial curvature is positive, it's a hypersphere, not a sphere, with a radius that's unrelated to the CMB radius.

Your argument that the CMB radius should be 13.8 Gly only works in flat spacetime and inertial coordinates. In fact the radius of the sphere that emitted the CMB was about 42 Mly. At the present cosmological time, it should have expanded to a radius of about 46 Gly, but we can't see that. The ratio between those values is the redshift (1+z ≈ 1100).

• We have no idea if the universe is infinite or not. We have no data that rules it out, but we also have no data that rules it in (i.e. that rules out the universe being finite). Within our current knowledge, the universe could be finite or infinite. There's currently no way to tell. Commented Sep 25, 2023 at 0:41
• @CJDennis I didn't mean to say otherwise. "For all we know" = "It may be that". What I think is ruled out by data ($Ω_k$ and matching circles) is just that the universe is so small that CMB light could have circumnavigated it. Commented Sep 25, 2023 at 0:53
• Sure. A closer reading shows you did indeed say that. Instead of "For all we know …" I read it as "We know …". There's a lot of talk on this question about the universe being infinite. A comment on the question "The universe is probably infinite", and your answer "For all we know the universe is infinite in size", and another answer "the universe as a whole appears to be infinite". I think most scientists agree that the universe is larger than the observable universe which doesn't rule out either it being finite or infinite. Basically a lot of emphasis on infinite, no emphasis on finite. Commented Sep 25, 2023 at 1:09
• Interestingly, I don't think CMB light circumnavigating the universe is even possible in theory except in pretty exotic setups. In a matter/radiation-dominated closed universe, there's not enough time to circumnavigate before the universe collapses. It's only possible with dark energy if you tune things right -- I haven't thought too carefully about the precise conditions needed, but roughly the dark energy needs to be stabilizing the universe against collapse rather than driving accelerated expansion.
– Sten
Commented Sep 25, 2023 at 7:27
• @PM2Ring I think "the universe is probably infinite" is too strong. The evidence that $k\le 0$ is weak, and from $k\le 0$ it doesn't follow that the universe is infinite: you have to also assume that it's homogeneous and isotropic out to infinity, which seems dubious. Inflation may produce a homogeneous region a googolplex light years across, but that's just peanuts to infinity. Commented Sep 26, 2023 at 0:46

When people talk about the universe having been small in the past, they're properly talking about only the part of it that's currently observable. That was much smaller in the past, but the universe as a whole appears to be infinite and always has been. The expansion of the universe doesn't mean the total size gets larger (that's meaningless if it's infinite), it means all the stuff is moving apart (along with the geometry of the universe itself). The big bang occurred everywhere at once.

Over cosmological time, the CMB shows an expanding slice of the universe. The age of the universe when the CMB was emitted will always be the same, but the slice will get larger and larger.

• The universe appears to be very large (larger than we can observe). Commented Sep 25, 2023 at 6:50

From some comments of yours I don't understand when you say you want to know about 'the image' and not about the photons. The images we create are from the photons. 'The image' doesn't exist as a separate thing. The origin of the photons of the CMB as it would be seen from any point in the universe was a cloud of plasma at about 5000k that was the entirety of the universe when it was 379,000 years old. Different locations in our universe would see different images. A galaxy 100 million light years in one direction from us will see what we are seeing now in the opposite direction in about 100 million years, but shifted to even longer wavelengths.

The 379,000 years you mention is the time when the universe became transparent to photons of any sort, and that is the main way for us to observe it and what the CMB is. The thing is that since the universe is expanding. The CMB we see, and thus the images we create from it, is always from the time when the universe was 379,000 years old. Before that the universe was opaque so any photons would have been absorbed and re-emitted. Once the universe cooled enough to become transparent, photons were free to move about and we can gain information on what produced those photons by observing them.

As time goes by when we look at the CMB we are seeing further across the universe as it was at that time. Photons from parts of the universe that were closer to us would have long passed us by. Photons from parts of the universe that were further away from us are still traveling towards us. Photons from parts of the universe much further away will never get to us because the universe is expanding too quickly. We can also see photons from closer objects that generated or reflected them after the universe became transparent, but that is not the CMB.

Right after the universe became transparent the photons would not have been microwaves, they would have appeared with shorter wavelengths. This answer seems to say they would have been around 5000k, which is visible light. It's complicated as there was a long period before reionization when the universe was still opaque to visible light at large scales.