This lab involves using maps of the CMB to estimate the curvature of space.
The CMB is light which comes to us from the "surface of the cosmic fireball". This light has been traveling through space in straight lines ever since the Universe was 380,000 years old. The Universe is now about 13.8 billion years old. So this light comes to us from when the Universe was 1/30,000th of it's present age.
Early on the Universe was super hot gas called plasma filled with blindingly bright light. Plasma is not transparent to light, so the light rays kept bouncing around having their directions changed - getting "scattered" around by the plasma. As the Universe expanded it cooled. 380,000 years after the beginning it had cooled enough that the plasma became ordinary gas. Ordinary gas is transparent to light so after this time the light rays traveled in straight lines. So we call the time 380,000 years after the beginning "last scattering".
There are CMB light rays all through the Universe. But the ones arriving at Earth today from all directions are the ones which set out from a spherical shell around Earth 13.8 billion years ago.
The present day Universe is very "lumpy" - the density of matter in the Earth or a star is enormously greater than the density of the wispy gas in the great voids in between the galaxies. But the plasma of the early Universe was extremely smooth - the densest clumps were only slightly more dense than the least dense regions in between. Nevertheless the lumps were slightly hotter and the regions in between slightly cooler.
The hotter regions emitted slightly more light than the cooler regions. This leads to an amazing fact: if we can measure the brightness pattern of the CMB over the sky we are actually measuring the density of the Universe on a spherical shell around where Earth is now as it was 380,000 years after the big bang. A kind of "core sample" from a very early time.
Since last scattering the Universe has continued to cool and expand - by about a factor of 1000. The hot gas went on to form much denser clumps called galaxies, and eventually stars and planets and us. The blinding white light rays have meanwhile being streaming along unimpeded, as space stretched under them shifting them way down in the microwave region of the spectrum.
It is very hard to build a microwave telescope sensitive enough to measure the brightness pattern of the CMB. And to get the whole sky the best way is put the telescope in space far from the Earth - so it doesn't block the view. Currently the best such telescope ever built is operating. It is called WMAP. The picture below shows the map it has made of the CMB. The red regions are slightly hotter and the blue regions slightly colder. Imagine that Earth is at the center of this sphere - we are seeing the clumps and anti-clumps on a shell cut through the 3D structure of the Universe when it was 30,0000 times younger than it is now. Which is pretty amazing information to be able to have when you think about it.
Look at the map above. Looks like a bit of a mess doesn't it? That's because the infant Universe was very unstructured and chaotic. There are blobs of all different sizes (i.e. there are clusters of blobs). Nevertheless it is pretty clear that there is a size of blob which is most common.
While the infant Universe was still hot plasma it was a bit like a quivering lumpy jello. A region which found itself a bit denser than the areas around it would start to collapse in on itself due to its own self-gravity. The size of the collapsed regions grew over time as the pressure wave (sound wave) moved out from the center. i.e. as material has time to "realize" that there was a clump nearby and start to fall towards it. But then suddenly the Universe cooled enough to become neutral gas and the light rays became "detached". It's easy to see why the most common size of blobs and anti-blobs (hot and cold regions) corresponds to the distance sound had had time to travel in 380,000 years. We call this distance the "sound horizon".
What we actually measure on the CMB sky is the angular size of the blobs - i.e. the blob size in degrees. But the sound horizon is a physical size - in light years. We can exploit this to measure the curvature of the space, and therefore the density of the Universe. In the figure below the solid red bar to left in each case is a typical hot or cold blob. The thin red lines with arrows are the paths that light from the edges of the blob takes to reach the observer at the right in each case. The middle possibility is where space is "flat". i.e. it behaves like a flat piece of paper, a triangle is a triangle, and the blob subtends the angle one would normally expect given its size and distance from us. In the left example space is closed or positively curved - so the triangle behaves like the one on the surface of sphere in last weeks lab. Try to understand how the curvature of the line exaggerates the angular size of the blob making it look bigger than it actually is. The right case shows the third logical possibility - open, or negatively curved space. Notice how the size of the blob is "dexaggerated" and it looks smaller than it actually is. The small maps at the bottom of the figure show how a small region of the CMB sky might look in each case.
Draw a triangle (i.e. assume that space is flat). What is the size of the blob in light years? What is the distance from us in light years? There is a wrinkle here - we want to draw this imaginary triangle as it would "look today". So we have to take into account that the Universe has expanded by a factor of 1000 since the CMB light rays started on their long journey to us. Calculate the angle that we expect a typical hot or cold blob to subtend on the sky today. This is a very simplified calculation but the answer is not so far from correct.
One of the reasons cosmologists love the CMB so much is that the physics of the plasma Universe was very simple. We can make accurate calculations of what we expect the CMB sky to look like for a given type of Universe which we might be in. By "given type of Universe" we mean how much of the various types of stuff has it got in it, how fast is it expanding at the present day etc. The most important thing for determining what the CMB sky map will look like is to know what the total density of the Universe is - i.e. is it closed, flat or open.
Note that when we say we can calculate what we expect the CMB sky to look like we only mean how many blobs of different sizes we expect - the quality of the pattern. The exact pattern itself is not something we can calculate - it's random.
Now we are going to look at a real map of a small patch of sky - a zoom in region 10 degree by 10 degrees - and compare it to some simulated maps of what we might expect for a range of different Universal densities. Here is the real map - it is taken from an experiment called BOOMERanG.
Click on the image below to see the simulated maps closer up. To aid the comparison you probably want to open this in another browser window. Right click in the image and select "open link in new window".
When making the comparison note that we are only expecting the quality of the maps to be similar - their "blobiness" - we are not looking for maps which actually have the same structure. Also note that good though the telescopes are they are not perfect - the real map contains noise and other imperfections which the simulations do not.
What is your estimate for the density of the Universe compared to the critical density. Is high school geometry saved?
If you want to read more about this stuff Wayne Hu's website is really good.