Now there is a bit of a problem or a complication here. We've said that a given measurement like the microwave background or the acoustic oscillation to the galaxies today or supernovae tell you a particular cosmological parameter but it's not quite that simple is it? No there are uncertainties and the uncertainties are actually pretty big in any of the given experiments. So let's take the most recent measurements of the cosmological constant and the total matter density of the universe from supernovae which are shown here in this that blue or purple I'm colorblind. It's blue. It's hazardous being an astronomer being colorblind. So what this is saying is this inner line here is saying that we're two thirds are actually 68.3% sure that the real answer lies in here and for the cosmic microwave background it turns out we're 68% in this little narrow bit. It's very small this way but it's very long this way. So we really not actually sure what's going on except for from here to here. So this graph to make clear this is telling you the amount of omega matter and the measure of the universe is telling you the amount of dark energy. And what this is saying is that if you just had the microwave background measurements it could be here which would be 70% matter and what 20% dark energy or it could be up here so 80% and 20% basically what this is telling us they measure the universe is geometrically flat so it's telling you the sum of these must add up to one but it's not telling you actually which combination any combination adds up pretty close to one. It's somewhere wrong here it's acceptable but it is absolutely really out there. It couldn't be there. It's going to be some moments narrowest stripe. Right so you have what we say we would say covariance if you want of the parameters or it means you measure something but you haven't measured quite what you want which is what's omega matter or what's omega lambda you measure the combination together. This is often called degeneracy in the sense that what you know is some combination of two things not one by itself. So we know if we knew the value of one we could calculate the other but we don't know which combination along this line is sitting there but conveniently the supernovae are degenerate this direction that is we measure combination of omega lambda and omega matter in this direction and the cosmic microwave background is it almost at 90 degrees not quite but close. So that means that if we take this and this we get a really accurate number together which is going to be sort of in here together. On top of that we also have the bearing on acoustic oscillation measurements which turn out to be something sort of in this direction and when we add those together we get this tiny little area where everything is consistent together and so we are able to zero in to a very precise value of omega matter and omega lambda it turns out. I know one of the surveys by itself would be able to do that it's not even a combination of them that you can get this very precise. That's true and so that makes it very useful. It should note though that if you want to get rid of the cosmological constant you really can do it with any one of these experiments or sorry if you if you you can't none of these experiments allow the cosmological constant not to exist all of them required. And we're lucky that they all overlap so we've got this one on this one that overlap over here and then we've got the side of the thing that's not shown from the bearing on acoustic oscillations and it luckily goes up there if it went up over here there would be no place where all three of these things matched. And then we would know we would have a problem and that would have been exciting although it would mean we wouldn't understand what's going on very well. Here's another example of one of these plots now a plotting w which remember is the equation of state parameters telling you whether the dark energy becomes bigger or lower density as time as universe expands against omega matter and he got the microwave background measurements he got supernova measurements. And they cross again and again we also have that bearing on acoustic oscillation measurements which cross through here as well. So once again when we add it all together you get this nice little gray area where we put all the information together and it's quite interesting to see where it lands. Mega matter of about point three and the equation of state parameter of minus one. Just what Einstein said. What Einstein said. So it looks like whatever is going on that same story of 30% of the universe being omega matter and 70% is this stuff that has an equation of state almost exactly what Einstein said which is stuff that does not change over time. So if we're rolling down the Mexican hat we're very close to the top and that would be unfortunate place to be because it's kind of hard to tell that we're there in any sensible way. So we can put all these things together and for example take stock of our universe. This is what our universe is made of and we know from this combination of things that it's about just over 30% matter and just under 70% dark energy dark energy with an equation of state parameter consistent with minus one. And we also know from the primordial nucleus synthesis the deuterium to hydrogen ratio that it's about 4.9% ordinary matter and the rest must be something that's not made of barrions. So some weirdos of atomic particle. Yes and so it's a funny universe but geez we have a lot of precision here and I should say that I think maybe there's still a little bit of uncertainty. This is the best measurement we have right now but there's still some uncertainty whether or not we might have some little errors creeping in in some of the experiments and so face value this is the best answer and maybe we can talk a little later on about how robust these numbers are. So what universe do we live in? We live in a universe that's flat within 1% or maybe even a bit better than that now. It's better than a half a percent and pretty much there's no way around that. All of the measurements even with the uncertainties really now with the cosmic microwave background that that answer seems to be right. I mean the age of the universe with the precision unmatched since Archbishop Usher said it was 4,04BC. Yeah on October. 13.798 billion years plus or minus .037 that is incredible precision. So one thing we're not sure about is whether or not the universe is open, eternal or infinite because it's on that knife edge where you can't tell. So that's an interesting place to be and of course that is what inflation said we would be close to but it doesn't actually tell us the real answer. So let's tell you if you open or close it does tell you if you're internal because you've got a cosmic or constant in there. It's going to keep on going forever unless it decays. And that Mexican hat allows that to occur in the future. And I should say I had a bet with my office mate Sean Carroll. Hello Sean. Sean is a well-known cosmologist to this day and when we were graduate students in 1991 I bet him a ball will a very nice port that in 2011, 20 years from the day we made the bet that we would not be able to measure the geometry of the universe or omega to better than 30%. And here we are in 2014 and it turns out even in 2011 and the time of our bet we could do it 30 times better than I was expecting. So I lost the bet but Sean shared the port with me very nice. One thing that's still a bit of controversy over is the value of Hubble coast of the expansion right now. Here's a variety of different recent measurements. So if you have measurements from the different microwave backgrounds like lights and from sea fides and other things like that. And they are jumping around a bit. I mean the air ball is all over the lab. But there is a little bit of a systematic error where these are all measuring how fast the universe is expanding nearby. And these are using the cosmic microwave background to go through and take a model where you take what's happening now and shrink it to a factor of 10 to the 9 more dense in the past where you have these acoustic oscillations bouncing around. And there seems to be a little bit of difference. It's not huge. We like to call this tension which makes life interesting. I mean so we have something else to do. I should say for example this measurement though has already moved a little bit down since the time of this diagram. So that's resolved it a little bit. And there is some controversy even between the Planck and the WMAP teams we can talk about later on. But it's still amazing. We've not believed 20 years ago that we could measure anything in cosmology to anything like these positions. We truly live an era of precision cosmology.