[BLANK_AUDIO]. So, we have used our giant telescope to survey the sky every few nights, we have used CCD technology in order to record the light that's collected from those telescopes. We've used our computers to analyze the petabytes of data that's been produced to look for objects that go bang, change their brightness. And we've used spectroscopy in order to get redshifts for those objects, to verify that we've found the standard candle supernova 1a that we want and by measuring the brightness, we've also got a measurement of distance. How we're going to put all this data together now in order to unravel the mysteries of dark energy in our universe. Okay, if you cast your mind back to week four, when we were thinking about the expanding universe and that galaxies moving away from us will have a redshift. I'm going to give you a formula for that this week. We use the letter z for redshift, and it's equal to the wavelength of light that we observe from a galaxy minus the wavelength that it was emitted at, divided by the wavelength that it was emitted at. Now the light that's coming from galaxies just comes from atomic transitions. So, we know the wavelength that the light was emitted at quite accurately because we can measure that in the lab. And we can use the spectrographs that Andy's been telling you about to measure the wavelength of the light that we observe. So for any galaxy, if we image it with a spectrograph we can calculate it's redshift. Now we've been talking about supernovae and how we can use them as a standard candle to measure distances. So, if we have enough supernovae observations then we can also get distance for these galaxies and we can compare the distance and the redshift and this is what Edwin Hubble did back in the 1920s, he looked at quite nearby galaxies. Just drawing on his data there, and what he found was a really nice linear relationship between redshift and distance. He found that the distance was equal to the speed of light divided by what's now called the Hubble constant times the redshift and this relationship works incredibly well at small distances away from us. Now, if we're wanting to probe the expansion of the universe to try and understand the mysterious dark energy, we're going to have to look for that at slightly higher redshifts and then we need a slightly more complicated equation that takes into account the changing expansion of the universe. And this equation I've written out here works for redshifts less than about one. If you want to go higher redshifts than that you need more terms in here. Okay, what have I written down here? I've got this parameter q in here. Now q tells me about what's happening to the expansion of the Universe. Now if q is less than 0, then we have a universe with dark energy in it and it's causing accelerated expansion and you can see that here in this equation if q is less than 0 then for a fixed redshift, my galaxy will be further away. Let's look at the other case where q is greater than 0. In this case the expansion is decelerating. So, I can draw these lines on my plot now. And let's just go out to a redshift of one which is where this equation works. And now in an accelerating universe with the dark energy, you find that this tends to tilt up compared to a decelerating universe which kind of flattens off. Now, how does the data look on this plot. Well it was a real shock I think to a lot of people when very high redshift supernovae were measured, and they were put on this plot because what they found was the data favoured a universe which was accelerating. And you can fit these curves to the data; use the full formula here not just the approximation that I've written down here. And what you find is that our universe is made up of 25% dark matter, 70% dark energy, and the rest 5% you and me, the stuff that we're made up of, baryons. I find that really staggering. Only 5% of the universe is made up of the stuff that we're made up of. The results you can see here are the most up to date data of supernovae 1a, and it was observations a bit like this that resulted in the Noble Prize for Physics back in 2011. There were two teams that painstakingly discovered supernova 1a measured their redshifts and distances, and used that data to infer that the expansion of our universe is accelerating. Now the graph that you can see here, there are different colored points for different data sets and each point plotted represents a single observation of a supernova explosion. Now there's a black line that you can see drawn through it and that's the distance redshift relationship that you would expect to see for universe filled with 25% dark matter, 70% dark energy and 5% baryons. Remember the baryons is the stuff that we can actually see. All of the observations that we have are currently pointing towards a universe that is filled with dark matter and dark energy. But what could this dark energy be? Well there are big regions of our Universe that are a vacuum. There's absolutely nothing there, a complete vacuum. Nothing there at all except for a swarm of virtual particles that can simply pop in and out of existence and in doing so, they add energy to the universe that fuels this expansion. And if you like you can think of this as a perpetual motion machine because the faster our universe expands, the more vacuum there is created, the more opportunity for these virtual particles to pop into existence, thereby fueling even more expansion. And this beautifully simple theory has a small problem because you can ask a partial physicist to calculate exactly how much energy this phenomenon would create and it is one with 120 zeros after it times bigger than the dark energy that we actually measure. So, this big difference between theory and observations is making people think up lots of other theories and there are many out there but I thought I'd share with you the one that I'm working on at the moment and that's maybe our model of gravity isn't quite right. Now, Newton first came up with his theory of gravity and I showed you the Principia last week where he outlined his universal theory of gravity. But then Einstein came along and said actually if we want to explain gravity on much larger scales we need to understand general relativity. It could be that in order to understand the universe on the cosmological scales that we can observe today, it could be that we need to go beyond Einstein's theory of general relativity. Maybe that will help us explain these mysterious observations of the dark universe.