How Big is the Unobservable Universe?

“Really, the fundamental, ultimate mystery — the only thing you need to know to understand the deepest metaphysical secrets — is this: that for every outside there is an inside and for every inside there is an outside, and although they are different, they go together.” –Alan Watts

We’ve talked, recently, about the scale of the Universe, and trust me, it’s huge.

Filled with hundreds of billions of giant, Milky Way-sized galaxies,

each of which contains nearly a trillion stars,

the whole thing is really, really big. And, after nearly 14 billion years of expansion since the big bang, the part of the Universe we can see — the observable Universe — is 93 billion light years across!

But there’s more Universe outside of what we see. Based on our best theories of how our Universe got here — the theory of inflation — we might be inclined to ask just how big the entire thing is!

After all, inflation takes some initial region of space, and regardless of its initial shape, size, or conditions, stretches it, and causes it to expand at an exponential rate!

This takes any initial Universe and makes it huge! Not just billions of times larger than it was initially, but googols upon googols of times larger! It stretches it flat, it makes it uniform, and even sows the seeds of what will someday grow into the stars and galaxies that fill our Universe today!

Well, let’s think about what inflation does. This super-rapid, exponential expansion causes the spacetime of the Universe to stretch flat, but also to expand to a much larger volume than it previously occupied.

Image credit: Ned Wright's cosmology tutorial.

That’s what inflation is. But how does inflation happen? To the best of our (admittedly limited, and highly theoretical) knowledge, the Universe inflates when it’s full of what we call vacuum energy.

But being full of vacuum energy is unstable, and the when the Universe slips down into a more stable state (like sliding down this hill in the picture above), that energy gets transformed into matter, antimatter and radiation, and gives us the hot big bang, and our modern Universe.

But there’s something else we need to think about here. The Universe, at a fundamental level, does all the weird things that quantum mechanics lets it do. And one of the most bizarre things about quantum mechanics is that if you take something like, say, an electron, and you put it somewhere (like in an orbit, below), when you look again at a later time, it isn’t going to be in the same place!

In physics language, we say that the quantum state spreads out over time! Now, here’s where it gets really bizarre. We’re going to put all three of these things together.

  1. The Universe is inflating, or expanding exponentially. This means we’re making “new space” at an ever-increasing rate. After one unit of time (t), we have one unit of space (V). After 2t, we have 4V. After 3t, we have 16V, and after 4t, we have 256V. In other words, we are making lots and lots of new space very quickly, at an ever increasing rate.
  2. The average vacuum energy is decreasing as we “slide down the hill.”
  3. But, the actual vacuum energy in any volume of space, V, has to deal with the fact that the wave-packet is spreading out!

So we’ve got a race happening: the average energy is trying to slide down the hill, but in some of these areas of space, the spreading of this wave-packet pushes us up the hill instead of down it!

When we put all three of these things together, what we get is the concept known as eternal inflation. The big idea is that what we call “our Universe” is just one place — which we can only see a part of — where we’ve successfully slid down the hill. But the vast majority of the “true” Universe, outside of our little pocket, is still inflating, and still expanding exponentially!

Based on what we currently think about inflation, this means that the Universe is at least 10^(1030) times the size of our observable Universe! And good luck living long enough to even write that number down. Thanks to Rob Knop for making me think about this, and isn’t that a mind-blowing thing to think about? All that we know, see, and observe is just one tiny region that slid down that hill fast enough to end inflation, but most of it just keeps on inflating forever and ever. Aren’t we the lucky ones?!