So we've seen the basic idea of the anthropic principle, that is, that our existence as observers already conditions and limits what we can expect to see about the universe around us. So I want to dig into this more deeply now and to see how these ideas have led us in modern cosmology to the idea of the multiverse. The motivation for this comes most strongly from problems with the vacuum energy that we've heard about. And there are two. We can articulate these just by looking at the history of the density of material in the universe. Density versus time. The vacuum energy, the dark energy stays constant as far as we can measure where as ordinary matter declines with time. So we live just slightly to the right of this, this equality crossover. And this defines what's called the 'why now?' problem. After all, it's clear that if we change the level of dark energy, I could mean its, I could arrange for its density to be unimportant, even up to today, or for the crossover to have been way in the past. There's also the question of the the size problem. The density of dark energy is about 6 times 10 to the -27 kilogrammes per cubic meter. It's remarkable that we actually know that number. But is it a sensible number? Is it an actual number? According to the arguments I rehearsed for you previously, about the uncertainty principle, you might expect that the energy density of the vacuum would be characteristic of the largest energy scale that we can imagine. The so called Planck scale, that characterizes quantum gravity. The energy scale at which you would need to treat gravity itself by quantum mechanics. This is an energy in the units that particle physicists love are 10 to the 19 GEV. Suffice it say that's many powers of 10 larger than the Large Hadron Collider at CERN can achieve, and via E=MC squared, that's a mass of 2 x 10 to the -8 kilogrammes. Which seems a very small mass, but by the units of particle physics, it's colossal. And, if you allow the calculation of vacuum energy to go up to this scale, you would predict the energy of the vacuum to be about 10 to the 100 kilogrammes per cubic meter. So, something seems deeply wrong here. The vacuum energy is far smaller than you might expect and it's becoming important to the universe just today, when we observe it. So, the question is, are these two puzzles related? So let's come back to the Bayesian language in discussing these vacuum problems. What we're really saying is that we don't like the low value of the vacuum energy. Its improbable in some sense. That's fine up to a point. That's Bayesian probability can be very controversial. People are unhappy about the idea of introducing elements of subjectivity. Now probability can of course be discussed in a much more concrete way, from relative frequencies. If I toss this coin I say the probability of heads is a half. What does that mean? Tails. Tails. [LAUGH] Tails. Hm, this is unlikely. Heads. There we go. If I keep on doing this 1,000 times, I'll probably get roughly 500 heads. So when we have an ensemble of experiments, probability is really well rooted and everybody understands what we mean. So the question is could we imagine that there's actually, in the same sense, an ensemble of universes? Well, it sounds a bit crazy but this is seriously discussed in modern cosmology. It's given the name the 'multiverse'. And you can think of this loosely as many copies of our universe but each with different levels of the vacuum density. So, this is the basic idea that perhaps the vacuum density that we observe is very rare and unusual in that most members of this ensemble have much larger values. But, would we be there to observe that value? As I just presented it, the multiverse probably seems pretty far fetched and speculative. But interestingly, it emerges naturally out of the modern theory of cosmological initial conditions. Which is Inflation. Inflation was designed in the early 1980s to solve some of the big problems about the Big Bang as I've related it so far. You'll remember, the universe expands, but there's no means of asking what happened at times before the initial singularity. Moreover, expansion itself has a strange uniformity. Which we call the horizon problem. You can see this for example with the microwave background. Where the sphere of last scattering at every point on it, the temperature is 2.7 kelvin plus or minus one part in a hundred thousand say. How did the universe set itself up to be this uniform? After all, at very early times, a point over here actually had not had time to send a light signal over there. So that these two points in space could agree to have the same temperature. So there's a lack of causal contact. So what we need to do is somehow, is to, stretch the causal scale. And this is what inflation does. The way to achieve the stretching of the universe is to make one simple guess, which is that, maybe the energy density of the vacuum was much larger at earlier times than it is at present. So, supposing if I plot density versus time. But instead of the vacuum energy always having the same value at some early time, it was much larger. What would happen then? Well the answer is that you could take a very small domain. Let's say even something that's of a sub-nuclear scale. Small enough that certainly there's time for causal processes to operate to make sure it's uniform. But, if the vacuum density dominates, it can accelerate. And so this small domain can be blown up, that it is inflated extremely large, while the domination of vacuum energy lasts. And you can reach a state, where within it you might have a tiny domain perhaps say, only one centimeter across. Much smaller than the overall inflated bubble. But, that could be the part of the universe that will eventually expand to be everything that we can see today. And so, that vacuum driven acceleration would automatically achieve the problem that the big bang lacks, that is, causal contact everywhere. Then the vacuum energy falls and we're into a normal universe. What does the scale factor history of this look like? R versus t. We used to have this: the decelerating and then inflecting and reaccelerating universe. So now we have to remove this part leading to the Big Bang. And say that, in fact, it was also accelerating then. So rather than being a singularity from a universe of, of infinitesimal size, the universe could have just been growing exponentially for an indeterminate time. So the universe is much older, which is another way of understanding how it could be so uniform. So this explains, everything explains how the big bang that we thought was there was an illusion. And all we need is to understand how the vacuum energy could change precipitously with time in this way. Well, in terms of varying the value of the vacuum density, it turns out that the physics we needed was on the shelf all along. So in some sense, the correct explanation for the origin of the universe was maybe created in the University of Edinburgh in the 1960s. Peter Higgs was trying to solve a problem of the origins of masses of elementary particles. In order to do this, he introduced into the universe a new ingredient, phi, that we call the Higgs field. By now, you may be fed up with hearing the word 'field'. What is a field? It's a thing that fills all the space. Do we know what it is? No. But we're familiar with the properties with things like electromagnetic fields. This is another one. So what are its properties? Well the main thing it does is it gives to space an energy density. And it does it as a value of the scalar field. And the function that Higgs came up with more or less looks like this. Like a cross section through the bottom of a wine bottle. So if you think of this dynamically, as if there was a little ball running up and down in a trough. The ball could be here, where V is high, or it could fall off and roll down to here, or oscillate around the bottom, where V is low. So, this is like low values of dark energy, high values of dark energy. So this Higgs field dynamics gives us exactly the mechanism we needed that's a way in which the effective value of the vacuum energy can change with time, and fall from a high value to a low value. Now, it turns out that when you calculate this through in detail, the Higgs field can't be itself the thing that we need in cosmology. So, but this idea was far too good to give up, so there's a new field invented called the inflaton. So, provided the inflaton has some sort of potential, like the Higgs field, we could understand how inflation could come about.