So welcome to the last lecture. And what we're going to do today is we essentially summarize

all of cosmology because all of cosmology can also be studied from the cosmic microwave

background. So usually having, well discussing the cosmic microwave background at the end

of a cosmology lecture is kind of a problem because in some sense it's one of the most

important topics. On the other hand, a lot of the things that people traditionally discuss

in the context of the cosmic microwave background we've already touched upon. So from some point

of view, this is kind of today the lecture that ties everything together and many of

the concepts that we discussed will show up again. So we already spoke about the cosmic

microwave background and this is the first map of the microwave background that was measured.

And by first map I mean the first map of the entire sky. This was done with the COBE satellite

and US satellite. What you see here is temperature fluctuations at a level of 18 microkelvins.

So this is already after the motion of the solar system has been subtracted off but what

you see here in the center still is one of the many foregrounds that make life difficult

when looking at the microwave background. This is synchrotron radiation from the Milky

Way. But already up here you see that there are temperature fluctuations in the background.

This is at a temperature of about 18 microkelvins. So the COBE satellite found that the CMB,

cosmic microwave background, is this perfect black body with 2.7 kelvins and these tiny

little temperature variations at a level of 10 to the minus 5. And so what we'll look

at today is where these temperature variations come from and what we can learn about the

universe as a whole from them. The answer will be pretty much everything that we know

about the universe is hidden in these temperature fluctuations. So you can measure most of the

cosmological parameters just by looking at this. It's a bit like you're having your

mobile phone and pointing it at some black and white weird dots and suddenly getting

lots of information that's encoded in there. And the microwave background is pretty much

the same thing. So we already spoke where the cosmic microwave

background came from. We had three electrons and three photons. They were coupled to each

other and that means effectively that the motion of the photons and the motion of the

electrons was pretty much the same. So for example, coupling between matter and radiation

also means that where you have higher concentrations of matter, you're also going to have higher

concentrations of photons. This might appear weird at the moment, but think about what

this coupling really means. This means that there are frequent scatters between electrons

and photons. So it's very difficult for photons to diffuse out of that small little closed

space because they're interacting and scattering of electrons all the time if you have an overdense

region. So it's possible in some sense to really keep photons at a certain place.

And then what happened was that the universe decided, now I'm cold enough and you had now

neutral hydrogen, suddenly the photons were able to stream freely away from the places

where they were hidden. And they streamed freely up to the point now today that they're

discovered. What that means is that the cosmic microwave

background gives us a snapshot of what the universe looked like at the time of decoupling.

Fossils were first hidden and were stuck to baryons in some place and then suddenly they

could stream freely. So what you see, these fluctuations that you see in the cosmic microwave

background, the temperature fluctuations, are a map of the fluctuations also in the

baryons. So by looking at the microwave background we learn something about the electrons.

So let's look at that in more detail in what we had yesterday. Very briefly I showed you

linear structure formation. So we started out a long time ago because we were fast.

With this figure here we calculated effectively from this motion of a test mass and how is

this test mass moving in response to an over density here. We were calculating, well I

showed you that one can calculate, I think is the fairer thing that we could calculate,

something that showed us that structures could grow or disappear.

Now as long as radiation is coupled to matter, these things will just move and grow together.