“The size of the universe is no more depressing than the size of a cow.” -David Deutsch
But it is bizarre, I’ll give you that. The most common scientific question I get asked is how, if the Universe is 13.7 billion years old, and the speed limit of the Universe is the speed of light, why do I say the observable Universe is 93 billion light years across?
In other words, why is this picture of the Universe wrong?
I’ve tried to answer this before, and so have others, but perhaps it’s time for another — more conceptual — attempt. This is one of the most mind-boggling things about relativity. From special relativity, you know that you can accelerate any mass to move faster and faster, up to but never quite reaching the speed of light.
The closer you get to the speed of light, the more lengths get contracted and time gets dilated.
But in general relativity, you are limited by the speed of light relative to your own location in spacetime.
And although it’s tempting to think of spacetime as a static grid, it isn’t.
Because if the Big Bang and General Relativity are both correct, then spacetime is expanding.
This might appear to you as galaxies moving away from us, and the farther away you look, the faster they appear to be moving, but that’s not what’s actually happening.
Rather than galaxies speeding away from us, like they would in an explosion, the galaxies themselves are stationary (which, for our purposes, means moving at less than 1,000 km/s), but the space between galaxies is expanding.
In other words, it’s not like an explosion; expansion is very different. Wherever matter isn’t densely clustered enough to us — like beyond our local group of galaxies — it appears to be moving away from us. And the farther away from us it is, the faster it appears to be moving away!
Believe it or not, when this phenomenon — the apparent expansion — was discovered by Hubble in 1929, Einstein’s General Relativity had already predicted that this would happen! In fact, it was one of the first solutions to General Relativity ever discovered.
Just like the galaxies painted on to the surface of this balloon aren’t moving but are getting farther apart, because the balloon is expanding, the real galaxies in the Universe are getting farther and farther away from one another (and, therefore, from us), but due to the expansion of spacetime.
So with this picture in mind, you then have to turn to General Relativity, and ask it what determines the expansion rate?
The answer is “the sum total of all your different energy sources” at any given time. Dark matter, normal matter, dark energy, photons, neutrinos, etc., it all matters. As you’ve just learned, dark energy is most important now, dark and normal matter were more important in the near past, and radiation (photons + neutrinos) were more important in the distant past.
It turns out that, perhaps counterintuitively, the scale of your Universe (i.e., the size of the observable Universe) is related to the speed of light multiplied by the age of the Universe, but isn’t exactly equal to it.
In a Universe filled with 100% radiation, the size of the observable Universe is twice that number; our observable Universe would be 27.4 billion light years in radius if that were the case.
In a Universe filled with 100% matter, the size of the observable Universe would be three times that number; our observable Universe would be 41.1 billion light years in radius in this case. And this is close, but not quite right.
Adding a little bit of dark energy — making the expansion accelerate in the recent past — makes the observable Universe just a bit larger, and pushes the size of the observable Universe up to 46.6 billion light years in radius. Double that (to get a diameter), and that’s why the Universe is 93 billion light years across!
But the stuff that’s 46.6 billion light years away now was much closer in the past, and the total distance that light has traveled to reach us is 13.7 billion light years; it’s just that the Universe has kept on expanding throughout that light’s journey.
That’s why the light gets redshifted; that’s why the galaxies look like they’re moving away from us. But what we’re seeing is actually the expansion of the Universe, and the expansion continues before the light was emitted, during its travels to us, and after we’ve received it; and that’s how the observable Universe can be 93 billion light years across, even though it’s only 13.7 billion years old!