Welcome back everyone. So what we are going to do now start we are going to start walking our way through the modern story of cosmology and to do that we are going to think about the players that were going to have and the stage on which the drama of cosmology is going to occur. So first we want to talk about go back to space-time and idea of of we are talked about this a little bit Einstein's idea from general relativity that there was not space and time that was separate but there was one unified entity, that we call space time. And that has as the possibility of having a shape. That there's the fabric of space time. So when we come to thinking about cosmology, what Einstein allowed us to do was being to think about the shape of the Universe as a whole. And what he was able to do through his equations was show that when we think about cosmologies what we're going to be very interested in is the curvature of the Universe. And we want to think about this as sort of a, a rubber sheet that can be bent in different ways and the response of that of the sheet to the mass that's in the Universe, is going to determine very much the fate and history, or the, the history of the Universe. So there are three possibilities, for the curvature of the, of space-time. And the first one is what we call positive curvature. And it's very much like a sphere. You imagine the surface of a ball. and, imagine like the surface of the Earth. And imagine drawing a triangle on the surface of the Earth. What would be at, if it was a large enough triangle what you'd find is that the geometry of that triangle would be very different from the geometry of drawing a triangle on on a flat sheet of paper. For example, the angles would be, would be if you added up the angles, it would add up to something that was larger than 180 degrees. Whereas we know about on a flat sheet of paper, the angles always add up to a 180 degrees. So does, the space could be cog Universe could be like at the surface of a sphere, an expanding sphere for, in particular. Now, people really like this idea, at least to imagine, because it gives you a way of answering that question of, What's at the edge of the universe, right? Everybody has this trouble of imagining you're traveling in your space ship. And you suddenly come to a brick wall at the edge of the Universe. So the really interesting thing about positive curvature is that the Universe would be bounded, but finite. So what that means is, is I got in my space ship, and I headed off in that direction I would eventually come back from this direction. That's because, just like in the surface of the Earth, I could start from San Fransisco and head west. And eventually I'd reach San Fransisco again from the east. So it's a nice way of thinking about Universe that can be finite but have no boundaries. But there's other kinds of curvature which don't have that nice property. For example, there's negative curvature where the Universe is sort of shaped like a saddle and this would be an infinite Universe. It would go on in all possible all, all three spatial dimensions would continue forever. And there's also the possibility of the Uniiverse being flat as well. And in that case it would also be an infinite Universe The space would continue on forever and if you took your spaceship and headed in that direction, you would keep heading in that direction. So these three different possibilities for space are an important distinction because the, what you're going to get, which of those possibilities you're going to get will depend upon the matter, the amount of matter and energy in the Universe. And the only way to really understand the fate of the Universe is to actually try and go out and measure that energy density, or directly try and measure the geometry of space. As we've talked about, the geometry of, say, a triangle would look different in the, in universe with positive curvature, no curvature, or a negative curvature. So if you can find some way to actually measure that geometry, then you'd also have a sense of what the whether the Universe was infinite or bounded or not. so, now it's important to understand that also in space, that, that space is filled with, we've talked about matter, but really it, space is filled with, fields. Fields of energy, electromagnetism, gravity, etcetera. And all these fields ultimately have to be quantum fields, and particularly when we think about the early universe. We can think about the Universe being filled with energy filled that are what we call quantum fields, that are responsible for creating particles, or particles are the discreet manifestation of these fields filling space and time. And so even the vacuum, even empty space, is full of these quantum fields. And you can get what are called virtual particles. Particles that sort of emerge and then are, go back to the, the background in a timescale so short that you can't actually see them. However, they do have an effect. So the vacuum is not empty space, but is actually a seething Tumult of virtual particles appearing and disappearing back, you know, into, into their quantum fields. And you can actually measure this. There's experiments you can do. Where you can put two plates next to each other. And measure the force between the plates. And it turns out that the vacuum energy is actually significant enough that you can actually make a measurement of it. So we're going to have to, this idea of a vacuum energy is going to be very important to us as we through the narrative of cosmology. Okay, let's go on. [BLANK_AUDIO]