# If the universe is finite in size, will the CMB eventually go dark?July 13, 2023 4:20 PM   Subscribe

A previous question helped me wrap my head around the Cosmic Microwave Background. One thing I learned is that the universe might be infinite in size, and might have always been infinite in size, and the math of the most popular model of the Big Bang assumes that it has always been infinite in size. And this leads to a followup question: If the universe isn't infinite in size, will the CMB eventually go dark?
posted by clawsoon to Science & Nature (9 answers total) 3 users marked this as a favorite

Best answer: Imagine extrapolating a light-ray back in time, starting from our current time & place. As we trace its history back, one of two things can happen: either we get back close enough to the big bang that the Universe becomes opaque to photons, because it's too hot and so electrons & protons haven't yet recombined. These are the photons we see today as coming from the CMB.

Alternately, you can imagine that the light ray runs up against something where we can't extrapolate back further. From your question about the Universe being finite, you might be imagining some boundary to the Universe, for example. If the Universe had a boundary, then if you wait long enough, the light rays will start to reach us from the boundary (whatever that is) rather than from the era of recombination, and that would mean no CMB from that direction.

So the question is whether the Universe can be "finite" without "having a boundary". And the answer is yes, it can. For example, the surface of the Earth has a finite area, but it doesn't have a "boundary". You can travel in a straight line as far as you want without running into an "edge" of the Earth.

This gets a bit more complicated when you talk about our Universe, since it has three spatial dimensions rather than two like the Earth's surface does; but you can still mathematically describe spatial "shapes" for the Universe that have a finite volume but don't have a boundary. In such a Universe, we could still always trace a light ray back as far in time as we want (all the way to recombination) without impediment; it just might be that the ray has to "wrap around the Universe a few times" before it gets back to the recombination era. As an analogy here, you can travel an arbitrarily large distance in a straight line along the surface of the Earth; you just might have to wrap around the Earth a few times to do so.

The thing that would be distinct about a "finite-volume" Universe like this (one without a boundary) is that if you traced two different rays back far enough in time, they might take different paths "around" the Universe and be coming from the same part of the Universe at recombination. This would mean that two different parts of the CMB were actually due to the same fluctuations, and (eventually) we would start to see certain correlations in the CMB coming from wildly different directions. Cosmologists do look for these correlations but haven't found any yet, and this allows us to place bounds on idea that the Universe has a finite volume.
posted by Johnny Assay at 5:43 PM on July 13, 2023 [8 favorites]

Even if the universe turned out to be finite, I don't think the CMB could ever completely go to zero, due to conservation of energy.

The cosmic microwave background, being an example of black-body radiation, can also be described as a photon gas. In other words, it carries energy, and has a certain energy density. In the case of the CMB, its observed "temperature" of 2.7K corresponds to an energy density of about 4×10-14 J/m3. Very small, but not zero!

Imagine if the universe was finite and empty of matter: for example, a 3D hypersphere, analogous to the 2D surface of a sphere. Then those microwave photons would just travel for all eternity, looping around and around the hypersphere, keeping the same energy density forever.

(Note that I'm assuming a finite, unbounded universe, because the laws of physics as we know them assume that space is three-dimensional everywhere, with no "edges". If that assumption doesn't hold, then all bets are off.)

You might imagine that in a finite and non-empty universe, every CMB photon would eventually hit some opaque object and be absorbed. But even if that happens, the energy doesn't disappear -- it heats up the object slightly, and warm objects emit their own thermal radiation back into the universe. So in the absence of other effects, objects will eventually reach thermal equilibrium with the temperature of the CMB.

Note that if the universe expands, then the energy density of the background radiation decreases proportionately, and therefore the equilibrium temperature appears to "cool". But (maybe counterintuitively) this happens regardless of whether the universe is finite or infinite.
posted by teraflop at 6:19 PM on July 13, 2023 [2 favorites]

Energy isn't really conserved in an expanding universe (with dark energy it's actually increasing).

I suspect the CMB might eventually get so redshifted it would be impossible to detect. It's been redshifted by the expansion of space and dark energy is making that expansion accelerate, so it seems like there's nowhere for it to go but get redder and dimmer.

I don't think the answer depends on the finiteness of the universe; everything further away from us than our cosmological horizon can't affect us even in principle, and that is definitely finite.
posted by BungaDunga at 8:13 PM on July 13, 2023 [2 favorites]

Wikipedia says that "Redshift will stretch ancient, incoming photons (even gamma rays) to undetectably long wavelengths and low energies." and "The expansion of the universe slowly causes itself to cool down to absolute zero."

The CMB is dimmer and redder than most things already, so the CMB should also go dark, along with everything else.
posted by BungaDunga at 8:23 PM on July 13, 2023 [1 favorite]

If you have half an hour TIMELAPSE OF THE FUTURE: A Journey to the End of Time will take you there. If I read this correctly, their answer is - Yes - because eventually we reach a point where everything is the same temperature, time effectively stops and the cosmic disorder imposed by entropy cannot grow any more. Won't be for a while though
posted by rongorongo at 10:51 PM on July 13, 2023 [1 favorite]

Response by poster: So a finite, bounded universe might eventually see the CMB go dark for us, first in whichever direction the boundary is closest to us? But it sounds like there's no particular reason to believe that the universe is bounded?
posted by clawsoon at 12:31 AM on July 14, 2023

Basically, that's correct. But as teraflop noted, we don't have any good models for how a "boundary of the Universe" would behave. In fact, the mere existence of a boundary would violate the cosmological principle, since different points in the Universe would be differentiated by how close they are to the "edge". (Which doesn't mean it couldn't happen! But the principle has served us well in studying the Universe and abandoning it would be a big departure from that.)
posted by Johnny Assay at 4:28 AM on July 14, 2023 [1 favorite]

So a finite, bounded universe might eventually see the CMB go dark for us, first in whichever direction the boundary is closest to us?

I'm not sure that's right. As far as I know, the furthest thing we can see in every direction is approximately the same distance away. That is, our "cosmic horizon" is a spherical bubble many, many light-years across, centered on ourselves. If there's a physical edge to space it's even further away than that, so we can't measure it even in principle.

This horizon is an artifact of the finite speed of light, and will get bigger over time as more light reaches us. But there's a limit to this (caused by dark energy making the expansion accelerate), and unless the finite size of the universe just happens to be somewhere under that limit, we'll never see far enough to notice, because the edge of the universe will keep expanding faster than any light from it could reach us.

An infinite universe is probably indistinguishable from a universe that is merely too big for light from all of it to reach us before dark energy kicks in and really starts pulling things apart. You'd need a universe that was both finite and kinda small to be able to unambiguously be able to tell.
posted by BungaDunga at 6:51 AM on July 14, 2023 [3 favorites]

(oh, and by "small" I mean, if it's finite and small enough for us to eventually see an edge that we can't see now, we would have to be located pretty close to the center of the universe! Otherwise we'd already have noticed an edge)
posted by BungaDunga at 6:54 AM on July 14, 2023

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