So lets review where we've been so far. We've built up a picture of an expanding universe based on the key observation of the Hubble law (remote galaxies have spectra which are redshifted by an amount which depends on their distance - see lecture 11. Corroborating evidence comes from the microwave background and primordial nucleosysnthesis - both indicating that the universe in the past was hot and dense - see lecture 13. Additional evidence for an evolving universe are that the night sky is dark ( lecture 13), and that galaxy/quasar properties change as we look at large distances (remote in space means looking back in time to when galaxies were young - lecture 15). Small fluctuations in the microwave background are enough to grow by gravity into the galaxies and clusters of galaxies we see today ( lecture 15). But the large size scale on the sky of these tiny amplitude (1 part in 105) fluctuations is a problem for ideas about how they were formed from quantum fluctuations - these should have a tiny size scale as well as a tiny amplitude. This is the smoothness problem. Another problem is the uniformity of the microwave background - at early times the horizon was rather small so different bits of the sky shouldn't be at the same temperature! (horizon problem - lecture 15)
The ultimate fate of the universe then depends on how much gravity opposes the expansion - is there enough to eventually stop the expansion, so the universe re-collapses into a big crunch (Omega bigger than 1) . Or will the universe get slowed only a bit by gravity and continue expanding for ever (Omega less than 1). The dividing live between these two is a critical universe, whose expansion is exactly balanced by gravity (Omega=1) - see lecture 14. When we try and measure how much gravity there is then we come out with Omega of about 0.3 but most of this is in dark matter (edge on spiral galaxy - rotation curves, clusters of galaxies - galaxy velocities, X-ray hot gas, gravitational lensing). Primordial nucleosynthesis restricts the amount of this which can be made of normal material (protons/neutrons/electrons) to Omega between 0.02-0.03 (although it MAY be possible to get it as high as 0.07). So while a little of the dark matter which we see can be in normal matter (white dwarfs, brown dwarfs, cold gas) MOST of it has to be something else entirely (lecture 14). But theres a problem here too - perhaps more of a philisophical issue - why is omega so close to one ? (flatness problem - lecture 15)
All three of these problems (smoothness, horizon and flatness) can be solved by a period of extremely rapid inflation in the very early universe ( lecture 15) If the size scale of the universe increases really really rapidly at some point in teh very very early universe, then the size scale of tiny fluctuations gets blown up into a much larger size on the sky. And all bits of the sky were initially MUCH closer to each other, so could have been in communication with each other, so can be at the same temperature. And if you blow up the size of something tremendously then it looks flat!!
But this last point is a bit of a problem in itself. In a universe in which all we have is an initial expansion, which is simply slowed down by the universes own gravity, then the shape of space relates uniquesly to Omega. Flat space MUST have Omega=1, yet we MEASURE Omega=0.3. But we can DIRECTLY measure the shape of space if there is something far away whose size scale on the sky that we know - and there is! those tiny amplitude fluctuations in the microwave background have a known size scale on the sky - the size of the region which could communicate at the time the microwave background was formed. And we MEASURE space to be FLAT!!!
so now we have a direct contradiction. we measure Omega=0.3 from the mass and we measure that space is flat. If both observations are corect (and they do seem to be) then the underlying assumption that all we have in the universe is an initial expansion which is being decelerated by gravity MUST BE WRONG.
we can directly test this assumption by measureing the expansion rate of the universe now, and comparing it with the expansion rate some time in the past. When we look at remote galaxies we are looking back in time. And since gravity should have had less time to slow the expansion then the galaxies should be moving faster. The more gravity there is in the universe, the bigger the effect, so we can use this to measure the change in expansion rate. And conversely, in the limit where there is no matter in the universe, then there is nothing to slow down the expansion from its initial velocity - this is a very open universe, expanding forever at the same rate.
We can measure expansion velocity by looking at the redshift of remote galaxies. But then we need something other than hubbles law (which also uses redshift) to get distance=lookback time to a galaxy We saw that for nearby galaxies we could use 'standard candles'. Cepheids are the best as we think the period-luminosity relation is very tight so that for a given period there is a very well defined luminosity - combine with the inverse square law and the apparent brightness and get distance. But while cepheids are bright stars, they are only 1000x brighter than the Sun, so we can only identify them in relatively nearby galaxies. We used the apparent brightness of galaxies themselves, together with the width of their lines to calibrate their absolute luminosity (tully-fisher) to go out further, but not far enough! (review ways to get distances to galaxies in lecture 11). We need something brighter which is well defined. Supernovae are bright - they can outshine all the stars in a galaxy a few weeks to a month before they fade! there are two types. Type II are massive stars, and these are not that well defined as the star mass can be anything as long as its big! But there are also binary stars where there is a white dwarf accreting from a companion. when the accreted mass pushes the white dwarf over its maximum mass which can be held up by electron degeneracy pressure then the white dwarf implodes. So its a very well defined event, and should have (and appears to have) a very well defined luminosity. Go review supernovae!
Problem is finding them - they are very rare, maybe 1 per galaxy per hundred years. So you need to look at lots of faint galaxies. But it can be done and has been done and the results are comming in. Here are some pictures of them! Firstly, they are clearly inconsistent with the amount of gravitational deceleration you'd expect if the universe was simply an initial expansion declerated by gravity with enough matter density in the universe is enough to close it - Omega=1 is not allowed It looks a MORE like Omega=0.3, but even that isn't a particularly good description of the data. NONE of the models in which there is just the gravity of the universe decelerating an initial expansion really work. What the data REALLY want is that there is some gravity at about the level of Omega=0.3 (good, because we see this amount of gravity!!) BUT THAT THERE IS ALSO SOMETHING ELSE WHICH AFFECTS THE EXPANSION OF THE UNIVERSE. The data like an additional term, which corresponds to a continual ACCELERATION ie that the velocities in the past were less than we see now - this is the curve marked by the Lambda term!!
So, there is something else controlling the expansion of the universe AS WELL AS its own gravity slowing down an initial expansion. And this term is currently winning over the gravity of the entire universe, accelerating it more than gravity is decelerating it. The current best idea/guess/hypothesis as to what this SOMETHING is, is that its an energy/pressure associated with the vacuum, with empty spacetime. If it was simply an energy term then it simply adds to gravity as Einstein said that mass and energy are equivalent. so it would slow the universe down rather than speed it up....
But if this empty spacetime also has a PRESSURE associated with it then the numbers change. Think of 'normal' pressure that we see around us, like water turning to steam. The steam has some pressure associated with the expanding hot gas, and that pressure can be used to do work (eg the industrial revolution). We can get energy out. So pressure is a form of energy and Einstein said all forms of energy gravitate, so pressure ADDS to the gravitational field. And this normal pressure, if we trap gas in a box, but then allow it to expand to twice its size then we'd have half the pressure. But if we have some pressure associated with spacetime then if we have twice as big a box we'd have twice as much spacetime, and twice as much of this pressure. So it behaves in the opposite way to the 'normal' pressure we are used to thinking about - we call this negative pressure. And since it goes the other way it SUBTRACTS from the gravitational field. Which could power the accelerating expansion we see around us AND make the universe flat. This is called a cosmological constant, or dark energy, and is written as the capital greek letter Lambda. The curvature is given by Omega+Lambda and if Lambda=0.7 then we can have flat spacetime, and Omega(mass)=0.3.
so we have a universe whose mass is dominated by dark matter, and whose expansion is dominated by dark energy, and we don't really know what either ofthese things are (though we can guess!)
