Let us now take a more detailed look at the 1 of the, more or less, state of the art simulations using billions of particles done by Max Plank Institute for Astrophysics in Germany. This were done by the Volker Springel and his collaborators. The first movie will show gradual expansion of the universe as cosmic web forms. Then we will take a closer look at what structure looks like at the end. The simulation uses over ten billion particles, over a gigaparsec region of the universe. Now zooming in Mimics expansion of the universe, and as you can see that there is a gradual condensation of material into these filaments. Again, this is dark matter. If you could see dark matter in color, this is what it would look like. Now we are much too large scale to see detailed merging but we're zooming in closer and closer. Right now this is super cluster of galaxies scale and as we get closer in, you're going to see details that are more like current clusters of galaxies. For example, here this is about the size of the local super cluster. And zooming in further, we can see the gigantic dark halo forms which is really dark matter that belongs to a cluster of galaxies or giant galaxy with a lot of little dark matter halos that yet have to merge together. And now pulling out, just to see where this one little detail fits within the whole large simulation. Now, this is zooming in onto a particular small region of the final simulation, flying through it in 3D space, if you will. And to just to give you the sense of the richness of the structures that have been forming. This is frozen moment in time, it's the purpose is just to show you how complex 3 dimensional structure of this grid of dark matter really looks like. Remember, variants falling to the potential wells defined by the dark matter. So, if you could see stars as well, they would look somewhat like this but more condensed. Here we are rotating around a rich cluster of galaxies that is formed somewhere in one of the ANSIs peaks. This is not unlike c ore, or say, Virgo cluster of galaxies or comma cluster of galaxies, except, of course, the ANSIs are the dark matter particles. The different colors in this simulation indicate different densities. They're not representative of physical property or dark matter in any way. They're just There to make it easier to see the density contrast. And now, let us zoom out again from this cluster, and fly around it some more. As you can see, these modern simulations generate vast amounts of data as numerical output, and analyzing them is a very non-trivial problem. Then comparing them with observations of real universe is an even, trickier yet. Let's revisit some snapshots from the simulation, just to note some of the details. Here is a slice at the very large redshift. The contrast is not high yet. Dark matter potential wells are still collapsing, forming the first cores of galaxies, and clusters of galaxies. This corresponds to redshift 18.3. Roughly the time when we think the first stars may be forming. By about redshift 5.7, at which point, the universe is roughly a billion years old. You can see a much more defined mesh of filaments. Of dark matter with dense cores. Which are the halos of first galaxies. Into which baryons fall, and start making stars. By about redshift 1.4, structure is really well defined. This will be roughly the time when solar system has formed in 1 of these blobs that represent galaxies. And finally, this is how the universe would look today if you could see the dark matter. And zooming in, this would be roughly like the core of the variable cluster today. Now one of the problem with cold dark matter scenarios is, is that it predicts a large number of this tiny little dark narrow hallows and yet there is no real good observational evidence for them. Many different models have been proposed how to get rid of excess of small dark matter hallows. It's probably not a very difficult problem, but we still don't know for sure how it works. So one can try different simulations using different cosmologies which will then have different expansion rates, and so the large scale structure will be condensing in different ways as the function of redshift. Those can be then compared to observations from redshift surveys [at the variety of different redshifts. And not surprisingly, cold dark matter model seems to work the best or I should say cold dark matter model involving cosmological constant, the Lambda CVM model. You notice that the key process here is constant merges of smaller pieces into larger ones. Those are symptoms presented through so-called merger tree. Where it begins at the top each little branch responds to dark halo when 2 merge they become a larger branch and so on. Until the end of simulation you have one giant halo. You can track back which part of it came from where.This can be seen in simulation of the formation the local group and milky way at least the dark halo part there off. But Diemand et al shown in the following The simulation starts at the redshift of 12, a very low contrast. And then universe expands, dark matter condenses into lots and lots of little dark halos which keep merging to make the larger one, the progeniture of the, the milky way galaxy. There is a lot of chaotic merging that goes on. But on the other hand it can be tracked very well through numerical computation here because it's just a simple Newtonian gravitational physics, nothing else. And this is what it will look like at the end.