Last lecture we saw that one of the ways to see whether the Universe was open or closed was to look around at how much mass there is. And there were 3 possibilities - open, critical or closed. And if gravity and curved spacetime is all there is then these translate directly into the curvature of space so that critical is flat, closed is positively curved and open is negatively curved.
Lets take a closer look at how the mass is distributed. Suppose we find all the galaxies down to a certain brightness and look at their distribution on the sky, and then get spectra of all of them to get their redshift distance. But the sky is big, so its easiest to pick a slice of sky and study that. And galaxies are distributed in a very lumpy fashion as in the CFA survey which goes out to about 1 billion light years from our galaxy. But it has been done for the whole sky as well so we have a 3D picture of our local Universe. It is centred on the Milky Way, and shows the density of galaxies within a sphere of radius about 1 billion light years. Again its can see its rather lumpy. But we expect this - galaxies clump together because of gravity into structures called clusters of galaxies, and even clusters of galaxies clump together into superclusters. The big lumps on the 3D picture are superclusters containing about 1000 bright galaxies each. And there are now slice surveys that are going out quite a bit further than this, as in this one called the 2dF survey - The numbers of galaxies for a given apparent brightness falls off as we go further out due to the inverse square law!
So our current view has galaxies clustered together on filaments with big voids in between where there are fewer galaxies. Yet we said that the very early universe was a very smooth place - the cosmic microwave background is amazingly uniform in temperature. So how do we start out with something so smooth and get to something so lumpy ? Well, gravity is inherently very very non--linear. If we had regions in the very early universe that were ever so slightly more dense than the rest then these would have ever so slightly more gravity, so would attract the surrounding material and grow more dense, so they'd have even more gravity and attract even more material and get even more dense...... But if these regions were ever so slightly more dense then their cosmic microwave background radiation would have to come out through more gravity so it would be redshifted - slightly cooler. These temperature fluctuations in the cosmic microwave background measure on average 1 part in 100,000!! thats pretty small! But its enough! starting from these tiny fluctations, and with Omega=0.3 in dark matter we can make numerical models of the growth of structure in the Universe from these tiny beginnings to the present day. And these numerical simulations with Omega=0.3 (you want to look at the bottom right one which is lables OCDM) come out giving the same sort of lumpy pattern as is seen in the current Universe.
Neat! so can we use this to figure out what Omega is ? The sort of clustering we get looks slightly different if we have Omega=1 in dark matter (look at the one on the top right called SCDM) than if we have Omega=0.3. And Omega=0.3 gives something rather closer to what we see. Not exactly proof, but consistent with the measure of Omega from the local Universe.
And there is a considerable amount of evolution - as we look outwards then we are looking back in time becasue of the finite (though very fast) speed of light. So big telescopes look into the past. Given that the early universe was a rather different place - very hot and dense, then we might expect to see considerable evolution as we look back in time (ie further away in space). And indeed, we do see changes e.g. the density of active galaxies and quasars increases rapidly out to a redshift of around 2 - they were MUCH more abundant in the past than now. And galaxies were somewhat different when they were young.
But the fact that the microwave background fluctuations are so small DOES introduce a problem. Not with the level of structure we see today but with the size of the universe at very early times. Because the speed of light is finte and the universe has a finite past from the Big Bang, so we can only see out to a finite distance, which is the light travel time since the Big Bang. The universe itself may be inifinte, but we can only see out to a horizon which is the age of the universe in light years away! If we flatten the universe out on a piece of paper, put all spatial dimensions along the horizontal axis and have time going vertically then there is a light cone which defines what we can see of the universe - only things within the lightcone can be seen as only things within the light cone are within the distance that light can travel in the time allowed. So the horizon is getting bigger. But in the past it must have been smaller and when you do this, you find that at the time the microwave background was formed, 300,000 years after the big bang, then diametrically opposite bits of sky are not close enough together to ever have exchanged photons so its very very surprising that they are at such similar temperatures. The horizon then is only about 1 degree across the sky now (the sun is about half a degree in size) This is called the horizon problem.
And what causes the microwave background flutuations in the first place ? we can have a guess that they are some form of quantum fluctuation but these would be very small scale things, not on the size scales that we see.
And there are more problems too. why do we see Omega of order unity ? Both the density and critical density of the universe change rapidly with time as the universe expands, but they change in different ways. For Omega to be so close to unity now means that it must have been very very very very close to unity very soon after the big bang. This is the flatness problem.
A nice review of these problems is given in this cosmology tutorial (he talks you through the space-time diagrams in an expanding universe - I just cut straight to the one at the end in my lecture as you really don't want to know about the details!!)
One way out of all of these is to suppose that the early universe went through some fantastically rapid expansion - Inflation This would mean that in the past the universe was much much smaller, so things on opposite sides of our current sky DO get time to exchange photons and get into equilibrium. The expansion dramatically flattens out the curvature of the Universe and the dramatically expands the size of the fluctuations! Nice! but some addiational evidence that can provide a test of the theory would also be nice!!
