 Felly, ymgyrch o gynlluniaeth genedlaeth, cyfwyr ythyrnaeth rydych chi'n gallu cyfwyr cosmonogi. Yn ystod y dyfodol, yw Dysyddur yn 1917. Mae'n gwybod y universe yn ystod o'r cyfwyr yn ymddiol ac mae'n ddysgwyr o'r cyfwyr yn ymddir yng nghymru, ac mae'n ddysgwyr yng Nghymru. A'r ddysgwyr yng Nghymru eraill yn ymddiol. Mae'r ddysgwyr yn ymddiol, yn ymddiol, ac yn ystod o'r cyfnoddau cyffredinol, ac yn ystod o'r cyffredinol, yn y 1929, yw'r ysgrifennu o'r cyffredinol. Felly, mae cyffredinol yn ystod o'r cyffredinol, yn ystod o'r cyffredinol, yn y ffordd y teoriadau, yn ystod o'r cyffredinol. Mae'n ddweud i'ch gwneud y cyffredinol yn ystod o'r cyffredinol. Felly mae ystod o'r cyffredinol yn ystod o'r cyffredinol, yn ystod o'r cyffredinol, ac mae'n arddangos, fel y mae'r ysgrifennu ni, freidman, yn y 1922-24. Freidman oedd mas gwrthu gwneud bod gweld rwy'n ei gwylaw. Felly mae'n gwyllfa fwy ffordd i'r ffordd. Felly fy ffordd i'r cerddur victims o'r cyffredinol a'r ystod o'r cyffredinol. Rydym wedi eu wneud yma. Mae'r unig o'r unig yw ystyried. Fe'r unig o'r unig yw'r cyflwymon. Mae'n gwybodol. Mae'n gwybodol, gan weithio. Mae'n gwybodol, mae'r eich maen nhw eich gyfoen, oherwydd ymddangosai eu freiddem yn ei ddweud, mae'n cael ei ddweud o'r cyflwymon. Mae'r cwm, gyda'r cyflwymon a'r cyflwymon yn y ddiwedd gydag i'r hollwch ar y cyflwymon, oeddaeth 40 milion oedd. Aenstein's dynamics gan ystod y gallu ydych chi'n gweithio'r unig o'r ffyniteilio'r unig. Yr ydych chi'n gweithio'r unig o'r freidwyr oedd yr unig o'r gwaith yma yn ymgyrch chi'n gwirio'r ei funud. Fynnwch ar y ddechrau. Yn ei ffyniteilio, y pethau yn gweithio'r sdyn nhw'n gweithio. Mae'r unig o'r ffyniteilio. You can walk around it forever, you never come to a boundary, but you come back to your starting point. So the universe can be closed and have what's called positive curvature. Three-dimensional space can be curved in exactly the same sense. But what Friedman also showed was that you could have negative curvature. Now I can't draw you a picture of what that means, but curvature means that straightforward geometry doesn't apply, for example. We know that some of these three angles adds up to 180 degrees. That's not true in curved space. But the negative curved universe is what's called an open universe. And it would be infinite. So unlike a closed universe, which is finite, the universe of negative curvature would go on forever. And it's the density of the universe that turns one of these into another. There's a critical density, which is minute. It's about one atom per cubic metre. It's a better vacuum that we can make anywhere on earth. But that's enough material to turn an open universe into one that closes back in on itself. And every now and then you might see the symbol omega, which is the density divided by this critical value. And so we would say that omega equals one tells us to join a universe at the boundary between open and closed, which is flat. And strangely enough, from modern observations, this is where we seem to be. One of the ways that we learn about the early stages of the expanding universe is the fact that it was hot. So anybody who owns a bike appreciates this. You pump up your tires, you compress the air, it becomes hot. So the temperature of material in the expanding universe is actually proportional just to one over the size of the universe. The smaller it is, the higher the temperature. This means that early times the temperatures can be really extreme. So when the universe is about one minute old, the temperature is about a billion degrees. This means that nuclear reactions can happen, so nuclear can be assembled. So at higher temperatures they couldn't survive, so you had individual protons and neutrons. But as the universe cools below this threshold, these can come together to make a deuterium nucleus. And two deuterium nuclei can come together to make helium. Now what we see in the universe today is that all the stars contain roughly 25% by mass of helium. When this was first discovered early in the 20th century, it was unexplained. But it was then realized that this was an inevitable prediction of nuclear reactions in the early universe. Furthermore, by looking at the relic abundance of deuterium, you can measure the density of all ordinary material that participates in nuclear reactions today. The answer is something like 5% of the critical density. Remember, omega equals one was a universe that was flat. So ordinary atomic material we can be sure was being synthesized at the time when the universe was about one minute old. And we know today it's far short of closing the universe. Now a more direct way of probing the early hot universe is the fact that we can see it. If we look far enough away, we can see directly back to a time when the universe had that temperature. So there's radiation left over in the universe that comes from great distances. That's from a shell known as the last scattering shell. And that's because at great distances corresponding to early times as we look at it, material was ionized so that light can't propagate freely. Temperatures thousands of Kelvin, it's just like the surface of the sun. But eventually the universe cools to the point where atoms form. That is say for example with hydrogen, you have a proton and electron come together to make a single atom of hydrogen. That doesn't scatter light so effectively and then the radiation can propagate to see us. So over here it's say 3000 Kelvin, but it's at great distances and the expansion of the universe red shifts it. By the time it reaches us, it's a mere 2.7 Kelvin. So radiation of such a low temperature is characterized by radio waves at a wavelength of something like one millimeter. This is the so-called CMB, it stands for Cosmic Microwave Background. And this was found in 1960, well 1964 published in 1965 by Penzys and Wilson who received a Nobel Prize for this work even though it was a complete accident. And it's a strange irony that elsewhere in the world groups who understood this cosmological transition had predicted the existence of radiation and were preparing to search for it. In any case it is there and we can see back therefore to this era where the time is something like 400,000 years after the Big Bang. So we can get this close to the initial singularity with direct observations and that's extremely powerful.