So finally, let's turn to the formation of structures. How does all this happen? And this kind of encapsulates what we need to explain. When we look at cosmic micro-background, we're looking at a universe that's almost 3,890 years old. And the density fluctuations at that time, were a part in a million, less on smaller scales. Somehow, today you have large structure contrast on the order of hundred. Typically large scale structure stuff, this is above 100 times denser than me. And within galaxies themselves, the mean density of inside galaxies is million times higher than the mean density of the universe. So somehow we have to go from ten to the minus six to ten to the plus six in given number of billions of years. So we think that all of these started through some quantum fluctuations in the very early years. Particles are now looking pulse distribution anywhere, and then universe goes through a period of extremely rapid large expansion, it's called inflationary era, for which now there may be actual observational evidence, and so what used to be microscopic quantum fluctuations in energy density just due to the pair production and relation, is now inflated to the scale of clusters of galaxies. So that's where the fluctuations come from, and then, the question is, how are they going to evolve? And at first, they evolve just to the sub gravity. Denser spots will accrete more material, absorb smaller pieces. And this is what people who model structure formation do. You start with slightly non-uniform density field early on. You just let it go, simple Newtonian gravity, nothing else, and it makes structures just like those that we see. So as far as gravitational formation of structure goes, we got that. Now, turning gas into stars is a different business altogether. So the first question to ask is how long does it take for it to do that? Concept here is free fall time. If you have a density blob and you have test particle research, the blob is going to collapse under it's own gravity, and the outer most shells are always outer most shells. And so how long does it take for this particle to fall to the middle? And that's called a free fall time and is given by this simple formula. So for galaxies, typical like Milky Way, that's a few hundred million years, which is comparable to our internal rotation periods in the sun. For a cluster, that's more like several billions of years. So that tells you that galaxies have formed early on and clusters are still forming today. And that's exactly what simulations are telling us. And we see continuum from very slight density fluctuations and large scales to very dense clusters, so clusters of galaxies are still forming. Galaxies are more or less dying. And so simulations then can follow this in great detail whether or not they have dissipation. But also remember, there are all these filamentary structures. There's a sponge-like topology on large scales. Where did that come from? And that's actually fairly easy to understand. So consider a blob in the early universe that's over dense. It's not going to be spherically symmetric except by extreme random chance. Generally speaking, it would be better described as triaxial ellipsoid. They'll be different flattening in each of the three orthogonal axes. So the first listing is expanding with the expanding universe, then because it's got high enough cell gravity, turns around. It'll It will first turn around on shortest axis because that's the smallest r in m1, m2 or r squared, and so it will start falling down upon itself along the short axis first while still expanding in the other two. So from slightly flattened clause spherical blob, you get into the pancake, something that looks like a sheet. Now the intermediate axis turns around and it starts collapsing, so your pancake turns into a cigar. Something like a filament. And eventually, third axis collapses and you get quite a spherical blob which would be like a cluster of galaxies. So the origin of the topology is easy to understand, it's due to the expansion of the universe and that initial fluctuations are not spherically symmetric, and so we can see that and observe it, both observe it in the sky and model it, but we still don't have a good way of describing it, with numbers. Now, it turns out, the dark matter plays a crucial role in the way the fluctuations evolve. And different kinds of dark matter will work differently. So generally speaking, the smaller fluctuations will get erased, and they can get erased by different mechanisms. Particles flowing from one spot to another, and so on. How much depends on the kind of particles. If particles are very low mass and move at near or aphoristic speeds, then the density fluctuations can get very easily erased out to the scales that correspond to the speed of light times the time you give it to them. If on the other hand, dark matter is composed of heavy particles, they don't move very fast, they cannot travel very far, so they only erase the smaller fluctuations, not the big ones. In any case, you always eliminate smaller ones. The only question is how much and how efficient it is. And so we distinguish between simple hot dark matter, which is composed of very light particles, say like neutrinos, and the cold dark matter composed of submitcle particles like WIMPs. And hot dark matter is much more efficient in erasing small-scale fluctuations, because they are streaming at relativistic speeds. Cold dark matter does the same thing, but kind of slowly. Now, this is why there is a bend in the power spectrum that I've shown you. This is why there is a turn over at high special frequencies, which means small masses. And the shape of this is directly related to the type of the dark matter that's out there. And it turns out that cold dark matter wins. Hot dark matter would completely erase structures and scales of galaxies, all we would see is gigantic blobs of stuff. That's not what's observed. So in cold dark matter scenario, or CDM as everybody calls it, you start making small things first. You keep merging them together, building up ever larger structures, and that's called hierarchical structure formation. You start from smaller, go to bigger, and this keeps going on and on, you just move to ever larger scales. And all observations that we have pretty much follows by now. Well, that's all about gravity. Now what about dissipation? If you just look at gravity, if you look at those blobs in the early universe, they're overdense. They turn around, fall upon themselves, but while they're doing that, universe keeps expanding. And so if the universe wasn't expanding, they start with kinetic energy exactly equal to potential energy. And then they end up with viralized state where it's one half. And because potential energy isn't very proportionate to radius, that means they had to shrink by factor of two. And density will increase by two cubed, so eight, roughly a factor of 10. So if it was just gravitational flaps in stationary universe, we would have large scale overdensity as a factor of ten. But because the background's been expanding, by the time this is over, the density contrast ratio is more like 200. And lo and behold, that's exactly what we see. Remember I told you the overdensity of large scale structure is roughly factor of 100 relative to the mean. It's more in dense clusters, It's a little less in filaments. But that's about it. So this tells you, yeah, gravity's all you need to explain large scale structure. What about galaxies? They're million times denser than the background, not hundred times. So that means they had to dissipate extra energy in order to be able to shrink to small sizes to get this extra few orders of magnitude of density. So galaxies had to collapse by at least another factor of ten, maybe a little more, in order to achieve these densities. The only way they can do this is to get rid of this binding energy, so they have to radiate it away. And that process is called cooling. You can think of, say, electrons complex scattering or photons of micron background, or shock waves and collapsing galaxies releasing admission lines, and so on. There's any number of processes can be used to accomplish this. So dissipation is what makes galaxies distinct from large-scale structure. That's why galaxies are not just blobs of dark matter with bearings mixed in. But life is concentrated inside the dark fields. And nowadays, people do miracle simulations of this that incorporate feedback from stars, dissipation, the whole kit and caboodle. And those simulations work a little better than just pure gravity ones. But this is a messy process. Because all these dissapating processes are essentially atomic scale, atomic physics. And we're modeling things on scales of megaparsecs and so on. So in these simulations, even the best and the biggest ones, one particle that are following up maybe millions in solar masses. That's some particle, right? So it's a lot bigger than a proton. And so there’s a lot of kind of approximations going on in how that’s modeled, but by and large, the basic physics I think we understand. It’s just fairly messy process altogether.
