“The world owes you nothing. It was here first.” -Mark Twain
When you think about where all of this came from — back to the beginning of the Universe — there’s a good chance it makes you a little uncomfortable. For this week’s Ask Ethan, our one remaining column here on ScienceBlogs, our reader vvv asks a question that quite possibly many of you have wondered:
Why didn’t the universe collapse into a black hole right “at the moment of the big bang?”
And quite honestly, I’ve wondered a fair bit about this myself. Here’s why.
The Universe — as we see it right now — is full of stuff. Our galaxy is a tremendous swirl of stars, planets, gas, dust, and a huge halo of dark matter, containing between 200-400 billion stars and over a trillion times the mass of our Solar System, all told. And our galaxy is just one of maybe a trillion similar in size and scope, scattered throughout the Universe.
But as massive as the Universe is, that mass is spread out over a tremendous volume.
Our observable Universe is some 92 billion light-years in diameter, which is a ridiculous distance when you consider that what we typically consider “the end” of our Solar System — Pluto and the other Kuiper Belt objects — is just 0.06% of one light-year distant from our Sun! So we have a huge mass spread out over a huge volume, and it’s got to make you wonder about how they scale, relative to one another.
Well, our Sun has a mass of about 2 × 10^30 kg, which means it contains about 10^57 protons-and-neutrons in it. Given that there are about 10^24 solar masses worth of normal matter in the Universe, that gives us a total of 10^81 nucleons contained in a sphere of radius 46 billion light-years. If you work that out as a density, that comes to about two protons per cubic meter — on average — in the Universe today.
And that’s why, when you think back to the early stages of the Universe, when all this matter-and-energy was condensed into a teeny, tiny area smaller even than the size of our Solar System, you’ve got to wonder about vvv’s question.
Back when the Universe was just a picosecond old (after the Big Bang), all of this — the matter in all the stars, galaxies, clusters and supercluster in the Universe — was contained in a volume smaller than a sphere centered on the Sun with the radius of the Earth-Sun distance.
And, no offense to the idea of the entire Universe compressed into such a small volume, we know of black holes that already exist, that are a lot lower in mass than the entire Universe, that are already bigger than that!
This is the giant elliptical galaxy Messier 87, the largest galaxy within about 50 million light-years of us, or about 0.1% the radius of the observable Universe. It has a supermassive black hole at the center with a mass of 3.5 billion Suns, which means it has a Schwarzschild radius — or the radius from wherein light cannot escape — of about 10 billion kilometers, or around 70 times the Earth-Sun radius.
Well, if that much mass in that small a volume makes a black hole, then why would putting some 10^14 times that mass into an even smaller volume not make one? (And it very clearly didn’t; it made our Universe instead!)
Honestly, it almost did. The Universe, remember, is expanding as time goes on, and that the expansion rate is slowing down as we move farther and farther into the future. Back in the distant past, in the supremely early picoseconds of the Universe, the expansion rate was much, much, much larger than it is today. How much larger, you ask?
Today, the Universe expands at a rate of around 67 km/s/Mpc, which means that for every Megaparsec (Mpc, or about 3.26 million light years) something is distant from us, the space between us and it expands at a rate of 67 km/sec. Back when the Universe was about a picosecond old, that rate was closer to 10^46 km/s/Mpc! To put that in perspective, an expansion rate that large, today, would cause every atom on Earth to expand away from every other atom on Earth so quickly that they’d be more than a light-year distant from the next-nearest atom after just a single second!
There are two sides to the equation that governs this: on one side is H, or the Hubble expansion rate of the Universe, and on the other side is a whole bunch of stuff, but the most important thing is that variable ρ, which is the energy density of the Universe. If H and ρ are perfectly (or almost perfectly) balanced, the Universe can live for a very long time.
But a very tiny imbalance can lead to one of two very nasty fates.
If the expansion rate was just a tiny bit smaller back then, relative to the amount of matter-and-energy that was in it, we would have gotten a near-immediate collapse and implosion. That black hole fate — the best analogy we have for the big crunch scenario — would have happened catastrophically fast.
And if the expansion rate was just a tiny bit larger instead, no two atoms would ever have joined together in the Universe. Instead, things would have expanded so quickly that each subatomic particle would exist in what it perceived as its own Universe, with nothing around to interact with.
How different would it have had to have been to create that fate?
Keep going. It would take a finely-tuned difference of less than one part in 10^24 to keep the Universe alive for a timescale of 10 billion years or so. This means that a difference of even 0.00000001% of the expansion rate from the critical value would have been enough to cause the Universe to recollapse in less than a second if the expansion rate was too small, or to prevent a single lonely helium atom from ever forming in the Universe, if the expansion rate were instead too large.
But we got none of that; we got a Universe that appears to have been almost exactly at the critical balance between expansion and matter-and-radiation density, and the only tiny difference from that is due to the ever-so-slightly-non-zero cosmological constant our Universe possesses. We don’t have a full explanation for that last part, but you might enjoy learning what doesn’t explain it!
So thank you, vvv, for a great question for this week’s Ask Ethan column, and I hope this answer satisfies you! If any of you have a question or suggestion for a topic, ask away, and you’ll have two chances at having it answered: one here and one on the new blog over at Medium! See you there, and back here next week for another Ask Ethan!