How Fast Does the Universe Expand?

This post and its title were inspired by my answer to a Quora post, but I think it would be fun to do a sort of periodic astrophysics session for the public, using this as an inaugural post.

It is a personal belief of mine that what we learn is to be shared with others, not to be selfishly held. Certainly science itself is existentially justified by that and that alone. Knowledge is useless in a vacuum.

The quick and boring answer is about 2 attoHertz, or about 70 km/s per Mpc (kilometers per second per megaparsec). That means that things fly away from us 150,000 miles per hour faster every three million light years plus they are away from us.

However, there’s a ton of fascinating details in immediate view of this answer that should hopefully open your mind and educate you a bit of what we’re all really talking about when we talk about cosmological expansion that I’d like to share with you.

Scientific Globalism with Balloons

The problem with fully answering the question is that the intuitive thing to measure, how fast things in the universe are moving away from us, depends on how far out they are. So we can’t give a good, general answer for the whole universe that way.

To visualize the problem, think of a balloon inflating. Imagine we’re little observers watching that from a particular point on the balloon, as opposed to being normal humans not being on the balloon but watching it from outside because of course we would.

From our little spot on the stretching elastic, the parts of the balloon near us seem to move away the slowest; the parts of the balloon far away from us seem to move away the fastest. There’s nothing mysterious, it’s just literally where the points are on the balloon relative to us that matters. This is the exact same idea of why things in the universe that are further away to begin with seem to move faster away from us as part of the universe’s expansion. There’s a lot of exotic things about cosmology, relativity, astrophysics, etc. While trippy, this isn’t one of them.

However with the question remaining unanswered, the normal Us not being balloon creatures would look at a balloon inflating and clearly have an intuition for different possible rates of inflating it. You could take your time and bore everyone, rush it (and probably pop it), or somewhere in between. The idea is clearly solid. The trick is to find some metric that’s general, global: that doesn’t depend on measuring any particular spot on the balloon.

Well, one way to do this is if you assume that the nature of the balloon expanding is basically the same all over it. A counterfactual would help illustrate this. If it wasn’t true that the balloon expands in the same way everywhere, in particular if this absolute speed we’re seeking varied if you looked one way from your little observers’ position as opposed to another, then the balloon is expanding at different absolute rates in different spots. Just as you can tell that’s not what’s happening when you blow up a balloon at a birthday party, because it doesn’t end up all weirdly lumpy but smoothly round, we can tell that’s not what’s happening in the observable universe with high confidence.

So if that assumption is safe, which it seems to be, then you can get a rate for the inflation/expansion that isn’t dependent on which part of the balloon (or, to roll back the analogy, the universe) you’re talking about, but is instead global. That’s what you seem to be after.

The trick we can use then is simple. Divide out the velocity of the object/point moving away by the distance it is away from our point of observation, thus removing any factor of location in the resulting number. More technically, we’re cancelling physical dimensions of space and leaving only units of time. The number we’ve arrived at is a simple rate, a frequency just like the cycling of radio waves. And if you notice, it has to be true for the entirety of the inflating/expanding object assuming it was in nature the same everywhere, like the round balloon: which again like looking at a round balloon expansion being the same everywhere is an assumption well-supported by evidence.

Wow, Universe, You Don’t Even Look 13.8 Billion Years Old!

This then is the only notion of a global speed for the universe expanding that we have. The fair question is to try to more concretely and precisely ask, “Okay, but the rate of what?” Expansion, obviously, but since we’re being detailed, the way it is thought of (and what it is mathematically equivalent to) is the ratio of how fast what it means to be a meter changes versus what it means to be a meter. In other words, because the universe is expanding, a meter means something different at different times, so one thing we can do is think of a meter at any time in terms of a fraction of a meter today; the ratio then is asking how fast that fraction is changing with time. For the universal speed today, the “fraction” is 1, and so the ratio is just the speed of essentially how fast the fraction is changing away from 1 as we go into the future, i.e., how fast is a meter today becoming more than today’s meter tomorrow?

(Think of drawing a grid on the balloon before inflating it, and how the spacing between lines on the grid increases as you inflate it. That spacing is directly analogous to a meter, or any chosen unit of length.)

Like any speed, this rate at any time can be accelerated and decelerated, and we have detailed, empirical reasons to think it has done both. There was probably a hyper-rapid expansion rate at the very beginning of the observable universe (at the “Big Bang”) which then slowed way down to something slower than what we see today. Then with higher confidence still over the last twenty or so years we’ve observed a gradual acceleration that must have been occurring for some time now. We’ve avoided talking about general relativity, the engine driving the universe’s expansion, but it turns out that this phantom acceleration can be easily explained by an extra, unoffensive energy component that quite organically wouldn’t show up in, say, the physics of a black hole or something. For lack of a better name, it’s ended up being called “dark energy,” and that’s all dark energy is, the next time someone tries to play it up as being all exotic or whatever.

Regardless, we call this universal speed the Hubble parameter. If you try to flip it on its head since it’s a rate to estimate the age of the universe (the “period” if you will), you get a number less than the 13.8 billion years we’re always hearing about. That’s because, as mentioned, for a long time now the universe’s expansion has been accelerated so that it’s expanding faster now than it has been for most of its history. So to flip it on its head is to assume it’s been moving this fast the entire time, so you’ll end up guessing that it started later than it did: that the universe is younger than it is.

Edwin’s Tension

So to finally answer your question: what is it right now, during humanity’s cosmological epoch, the Hubble parameter (or colloquially “Hubble’s constant”)? We’re split between two different answers. One answer says about 2.2 attoHertz with some uncertainty, and the other says 2.4 attoHertz with some uncertainty. To bring back the “speed per distance” nature explicitly, we instead state these as 67 km/s per Mpc and 73 km/s per Mpc respectively.

The scientific community is famously split on the two answers, famous because the uncertainties don’t overlap. The disagreement can’t be explained by random error because someone was imprecise in their measurements or something. There is a fundamental, systemic difference in these two results, and it’s in trying to explain that difference that we end up in some very interesting territory.

We don’t know the answer to reconciling the results, so this next bit is speculative. One suggestion that’s getting a lot of attention (though perhaps unduly so) is that one measurement in its extrapolating calculations of the raw data is heavily reliant on assumptions otherwise based in evidence that the universe is, among other things, flat (meaning it obeys Euclidean geometry), the suggestion being that there may be a slight deviation from flatness. Also alluring is the idea of the dark energy not being static, as is essentially assumed by its unoffensive addition to general relativity, but instead either slowly changing over time, there being different kinds of dark energy in the earliest bits of the universe, stuff like that. More mundane but still interesting ideas include primordial magnetic fields creating knock-on effects in the observables underlying measurements in such a way that the difference in results is explained without touching the fundamental cosmology, which is always desirable in an Occam’s Razor sort of way.

But that’s where things stand right now. At a minimum, we stand to learn some cool new astrophysics in the history of the universe, at a maximum we may have to rewrite laws of physics. Just assume the latter is much more unlikely.

If I may, though, before I go, I’d like to extrapolate on something I said earlier.

It’s All A Big Bubble Universe Machine

One of the underlying assumptions to defining a global speed to the universe’s expansion was the nature of the expansion being basically the same everywhere. Observations strongly support this being true for what we can see out for tens of billions of light years out to that big wall of the cosmic microwave background. But let’s think for a second about a particular way this assumption ends up not being true, in a specific scenario set at the very beginning right at and after the Big Bang.

Imagine the round balloon again being inflated. But say that something about the minute fabric of the balloon’s fabric is randomly varying from place to place (the elastic tension, for example) so that it stretches differently place to place. For one, now the absolute rate no longer paints an accurate picture, as it’s not necessarily true anymore for any given point on the balloon. But also, the balloon now stretches out at different rates in different places, until eventually what’s holding different segments together breaks down.

The analogy itself breaks down here because the actual balloon then would just…pop. The actual theories I’m referring to ask instead what if the segments of the balloon essentially form…new balloons when they split off?

The random variations in the fabric of the balloon are quantum fluctuations in spacetime in conjunction with the hyper fast expansion at the beginning of the universe which I referred to earlier, and the new balloons then are new universes. Since their fragmentation was induced by the overall randomness, each end-state bubble universe then obeys for itself the sameness everywhere inside it. (The fluctuations are erased with expansion and time.) In particular one of those bubbles ends up being our universe in which we exist and have been observing that same expansional nature. This is one of two main ideas for how we might be living in a multiverse.

But that’s a story for another day.