So, the Universe started with a bang. Everything was hot, dense, and expanding.
It’s 13.7 billion years later now, and our Universe is cold and sparse. The temperature of the leftover glow from the big bang — which used to be over 10^30 degrees — is now down to 2.7 Kelvin, just barely above absolute zero. The Universe used to be denser than the center of the Sun. Now, on average, the density of the Universe is only about one proton per cubic meter, with mass clumped into stars and galaxies separated by trillions of miles.
But, for all of it, the Universe is still expanding. What’s amazing is, despite all of the things that could cause this expansion, there’s only one thing that the expansion rate depends on. Know what it is?
The energy density of the Universe. Or, in other words, the total amount of matter, radiation, neutrinos, and all other forms of energy in the entire Universe divided by the Universe’s volume. I’ll say it again: energy density is the only thing that determines the rate of expansion of the Universe.
This is remarkable, and here’s why. First off, the Universe could have existed in one of three ways. It could have been curved like a sphere (what we call positive), curved like a saddle (what we call negative), or completely flat (what we call zero curvature).
If the Universe were either positively or negatively curved, the three angles of triangles in space would not add up to 180 degrees! And the expansion rate would be dramatically changed by the presence of curvature. The fact that we have none is still a mystery for us, although perhaps inflation explains why.
The fact that the expansion rate depends on energy density means something else: at different times in the Universe, different things were important. Think about this: if you have a Universe where you double the volume, the matter density halves. Right? Same mass, twice the volume, therefore the density is half. I mean, look, the coins on the bigger ballon are clearly less dense, right? Same number of coins, but they’re spread out over a larger volume:
But radiation — things like light — not only dilute like matter does, it gets redshifted, which means its energy density drops faster than matter does. So when the Universe was very young and very hot and very dense, radiation was more important than matter was!
As the Universe cooled, matter became more important, and dominated the expansion rate for billions of years. But there’s something else in the Universe, something that doesn’t dilute as space expands. It appears that there’s an energy inherent in space itself, and this is what we call dark energy. Some people call it a cosmological constant. Why constant? Because its energy density never drops. Just a few billion years ago, dark energy became the dominant form of energy in the Universe. Matter gets less dense, but dark energy never does. If we graphed them all together — radiation, matter, and dark energy — you’d see which one dominated the expansion rate of the Universe.
And that’s it. That’s all that causes the Universe’s expansion: the total amount of energy that’s in it. From here to infinity, as far as we can tell, dark energy will continue to dominate the Universe.
Some of you are inclined towards math, and will want an equation that relates the Hubble expansion rate (H) to the energy density (ρ). Well, I hate getting too technical, so here you go: