So having learned that we can still see the Big Bang as something really hot with a temperature. And we can observe it with so called cosmic microwave background. At least we would like to know the mathematics behind this expanding universe. And if you're not familiar with the calculus, you can sort of skip this part entirely. But if you do have some background in it, you can follow through this with a fairly simple math, it turns out. So as it turns out, the expanded universe itself is governed by the force of gravity, Einstein's theory of, general relativity. So according to Einstein, it's actually a pretty simple thing. It's just like you keep a ball in your hand. You stand on the surface of the earth and throw it upwards, and initial thrust is the big bang. The way the ball keeps going up is the expansion of the universe. They follow exactly the same equation, it turns out. And then as you can imagine, if I throw a ball myself, then I can throw it very much with a high speed, so, it would eventually go up, slows down and stop, and come back down. Maybe the universe would do the same thing. It may start expanding, but at some point stops, and would come back down, and collapse. So that's one possibility for the fate of the universe. And we'll come back to this question later on. But as far as we can tell, anything that goes up should slow down, at least. So that's the equation for the cosmic expansion. So imagine the entire universe is this yellow thing. It has a certain mass big M. And it has the size, big R. And you place a probe, a tiny mass, up here. As a way of describing the motion of this whole universe. And you put this initial thrust and that's the big bang. You try to separate everything away from each other and that's how universe got started to expand. And then you look at these equations. If f equal m a, Newton's equation and this is universal gravitation f is given by this size of object. You put that together, and acceleration, if you know some calculus, is the second derivative of the position with respect to time. And just by looking at these three equations together, you find the last one. And as we remarked before, it doesn't depend on the mass of the object you're using to study it, because of the gravity, is actually the nature of space itself, it doesn't depend on the particular mass of your particular object. So that's the answer you get. And this negative sign here is telling you that universe must be slowing down. And given this, you have three possible fates. So if you use this equation, which is the same thing as the throwing the ball upwards, from the surface of the Earth. You can immediately see there are three possibilities. One of them is I said already the ball keeps going up to some extent but slows down and stops and then comes back down. So that's this green curve here. As time goes on, the universe gets bigger and bigger but slows down, stops here, and starts to come down, and then eventually ends up with the big collapse. And this is called the big crunch. The universe starts with the big bang, and may end up with the big crunch. But if you managed to throw your ball with incredible thrust, let's say you launch a rocket with it. So then you have such a big speed to begin with... That's beyond escape velocity we talked about before. Your rocket may escape the gravity of the Earth, and just may keep going farther and farther away from us. That possibility would be in this red curve. Initial thrust is so big, it keeps going away from the Earth with, pretty much, constant speed at the end of the day. So that would be a universe that keeps expanding forever. And that that would be this red curve here. In between the green curve and red curve, there is a possibility that the initial thrust is just right to escape the force of gravity. Then it just keeps going upwards, but slows down and down and down. And, and, and it almost stops. And that would be this blue curve. Either way universe keeps expanding forever, but with this choice, universe would have an end to it. So these are the three possible fates to the universe. And that's what we use to talk about since the expanding universe had been discovered. So that leads to this interesting question, is there an end, to the universe? And that would be a subject of my last lecture, so you should hold on, to wait for the answer about it. But one thing, if you are, are, well-versed enough with the mathematics, and this is something that would be useful to know. So with this equation. You can show immediately that this combination doesn't depend on time, it's a so called conserved quantity. If you take the time to both sides of the equation, you'll find it's zero using that equation in green. And this looks so much like the energy of the universe so to speak. And if this energy is positive, the corresponding situation that you can escape the gravity and keeps expanding in red curve. If energy is negative, it looks like you are trapped by gravity. If, if you go up, would eventually come down, that would correspond to green curve. And the blue curve corresponds to situation when this energy is exactly zero. So that's the way you can mathematically describe three possible fates of the universe. But either way, the universe seems to be slowing down. What would mean to us, if you're actually an observer looking into telescope, is a bright future for you. Because it is, universe is, is, is getting more and, slowly as time goes on. More things would come into your view as time goes on. And you will be able to observe more and more things as time goes on, so observation becomes more and more fun. If that's the right future for us, well, I will talk about that in later lectures. So that's the end of my first lecture today.
