“You must learn to talk clearly. The jargon of scientific terminology which rolls off your tongues is mental garbage.” –Martin H. Fischer
I’ve always thought that the Universe is absolutely amazing; that everything from the tiniest indivisible particles all the way up to the largest structures and superstructures making up the Universe has an amazing story to tell, if only we can figure out its secrets.
When I first learned some of them for myself, I was a graduate student, immersed in the minutiae and esoteric details of physics, astronomy and cosmology. While it was an absolutely fantastic experience for me, the clearer the picture I assembled in my head became, the further away I realized it was from most people’s picture of how it all worked. Writing this blog is one of the ways I hope to connect each of you — who want to know the story but don’t want to learn all of the excruciating details — with the Universe we all share.
The biggest question of all (for some, at least) is the question of large-scale structure formation: how did we go from a nearly perfectly uniform Universe to one full of galaxies, clusters, filaments and superclusters, as well as great, empty cosmic voids? Remember that our Universe isn’t just full of great concentrations of stuff, it’s also full of vast expanses of practically nothing!
In cosmology, it’s true: we have our own jargon for talking about such things. I (occasionally) receive negative treatment for not using “authentic” language, and am told I never say anything “smart.” For those of you who feel this way, here’s a “smart” sentence for you:
Cosmological perturbations grow according to the Mészáros Effect until the onset of nonlinearity.
Did I lose everyone yet? Good. Not “good” that I lost you; “good” that sentences like this are sentences you really, unless you’re also a physical cosmologist yourself (and one well-versed in structure formation, at that), shouldn’t understand. I never speak to non-cosmologists like this, and no scientist in general should ever, IMO, speak to anyone who isn’t also an expert in their specific sub-field in this kind of jargon. At least, not if your goal is to be understood and to help people learn something they might not have already known.
So now that you’ve heard the smart-sounding jargon, let’s tell you what it actually means, in English.
This is a photo of the ocean. In reality, the ocean extends downwards multiple miles (or kilometers) once you’re away from the continents, but from above the surface, all we can see are the tiny imperfections in the surface. Some spots may be a few inches (or centimeters) higher or lower than the average surface height, but the variations in height/depth are tiny compared to the actual height/depth of the water itself.
Believe it or not, this is how the Universe works when it’s very young, too.
Yes, some regions are slightly more dense than others, some regions are slightly less dense than others, and some regions are exactly the average density. However, the densest regions are only some 0.01% denser than average, and the least-dense regions are only some 0.01% less dense than average. (Those numbers are for departures from the mean that are so rare they only occur in one-in-ten-thousand regions of space.) These over-densities and under-densities are what it means to be a cosmological perturbation: deviations from the average!
But gravity is irresistible, even in a young Universe full of radiation.
Now the question becomes how do they grow? As the Universe expands, the amount of stuff — the number of protons, neutrons, electrons, and photons — remains constant, while the volume of the Universe increases. The density of both matter and radiation drops, but not at the same rate.
The matter density drops as the Universe expands, like coins taped to the surface of an expanding balloon. But the photons — the particles of light — also have their wavelength stretched, which means they get redshifted and lose energy, in addition to diluting as the Universe expands. In other words, radiation becomes less important, relative to matter, as the Universe expands.
And this is important for how over-dense and under-dense regions of the Universe grow.
Because that’s how these perturbations grow: in proportion to the ratio of the matter density to the radiation density. As the Universe doubles in size, the matter density doubles its ratio relative to the radiation density. The actual formula for the Mészáros effect (from Peter Mészáros, 1974) is that:
Or — in English — that if an initially over-dense region starts out as 0.01% more dense than average, it won’t grow substantially until matter begins to dominate radiation. (That happens when the Universe is a few thousand years old, and at matter-radiation equality, it becomes 0.025% more dense than average, or 250% the initial value.) Once that happens, each time the Universe expands to become 67% bigger than it previously was, that over-dense region will now be twice as dense (over the average) than it was before. An additional 67% expansion from matter-radiation equality means 0.05% denser than average, another 67% on top of that means 0.1% denser, and so on. Every nine times it increases in size by 67% means a growth of a factor of 100, relative to the average, of the magnitude of your over-density. (Or, conversely, a shrinking of your under-density.)
That’s what the Mészáros effect tells you. But it doesn’t grow like this forever; it can’t.
At some point, your over-dense regions become so dense that the over-dense part becomes almost as big as the average density itself! Just like the water wave, when your wave’s height above the surface is small compared to the depth beneath the ocean, the water simply exists as calm, unbroken waves.
As long as the over-dense part is small compared to the average density, you’ll grow the way I described above: according to the Mészáros effect. But when your waves get large relative to the depth of the ocean beneath them — or in the case of cosmological perturbations, when the over-density becomes a significant percentage of the average density — something breaks down.
For the water waves, they break and crash; for cosmological perturbations, they grow far faster than the Mészáros effect. We call this runaway growth, due to gravitational collapse, nonlinear structure formation. And that rapid gravitational collapse what gives us the structure in the Universe we see today.
Because of how these things grow, this means we see nonlinear structure on the smallest scales first (but only slightly), followed by the larger ones. In other words, we form stars before galaxies, galaxies before clusters, and clusters before superclusters!
A sentence like “Cosmological perturbations grow according to the Mészáros Effect until the onset of nonlinearity” might have a lot of meaning behind it, but it’s certainly no way to tell a story. And now that I’ve illustrated that point, I hope to never talk to you like that again.
Learning is for anyone who’s curious, and no one does any favors to the world by guarding knowledge. The only difference — from my point of view — that education should ever make is in the level-of-detail you can present to your audience. If you can’t explain it to someone, look inwards towards yourself, not outwards at them; it may be you who needs to understand it better.