We now turn, to the use of the cosmic 
microwave background, as a cosmological 
tool. 
This turns out to be, the most powerful 
tool in our arsenal today. 
And it's what really led us into the era 
of precision cosmology. 
The basic idea is as follows If we had 
something sufficiently large in the early 
universe that can be measured and we knew 
what redshift it was, then we could apply 
angular diameter test to it and constrain 
cosmological parameters from that and the 
largest possible thing we could think of 
would be The particle horizon at the 
time, which is the distance out to which 
causal connection can be established at 
the time that universe was that old. 
If we can infer the size of the particle 
horizon from physical reasons And, if we 
can somehow find its signature, in the 
microwave background, then we can perform 
the test. 
There will be density fluctuations, in 
the early universe, and those that are 
leftover from the quantum fluctuations, 
from even earlier times, in the history 
of the universe. 
And they would manifest themselves as 
slight variations in density. 
You can decompose those in series of 
waves overlapping and the matter would 
fall towards the densest parts and 
because the matter and radiation are 
tightly coupled before the micro backend 
was released, radiation would follow, 
inducing some slight Doppler shifts in 
its thermal emission. 
So when, microwave background is 
released, the decoupling stops, and, 
whatever pattern of fluctuation was there 
will remain frozen and observable today. 
Theory predicts that those who have 
amplitudes of some, parts in million of 
the present-day temperature, which is 2.7 
degree Kelvin, and so be very, very 
subtle effect to measure. 
So for a long time, cosmologists tried to 
measure these fluctuations, and finally 
they succeeded. 
There have been many experiments leading 
towards this, but the first really 
successful one, was a balloon born, micro 
background, measurement, from Antarctica 
called Boomerang. 
It was led by Andrew Lange and Paolo de 
Bernardis, and they were the first ones 
to have convincing measurement of this 
fluctuation at the scales that are 
relevant here, and the first ones to 
actually infer cosmological parameters 
from that. 
This was probably the single most 
important measurement at the time. 
At about the same time as the supernovae 
yielded the evidence for dark energy, and 
together they really opened this era of 
precision cosmology. 
Subsequently, WMAP satellite, which is 
Wilkinson Microwave Anisotropy Probe was 
launched And its purpose was to do this 
measurement even more precisely, and 
today the best results we have come from 
analysis of the data from WMAP. 
So here's how this works. 
If you were to take an image of the 
cosmic microwave background, it will be 
pretty uniform and so you have to turn 
the contrast now by factor of 1000. 
And then, you see that there is a dipole, 
due to the motion of the Milky Way 
relative to microwave background. 
If we then subtract dipole, and then 
turned a knob to even higher contrast to 
a million then we'll see fluctuations in 
the sky, a lot of them associated with 
the Milky Way galaxy, the foreground 
emission from synchrotron and dust and so 
on and after careful modelling which is 
very difficult and very delicate emission 
from the galaxy has to be removed and 
what's left is a pattern of density 
fluctuations in the early universe that 
have cosmological origin and that is the 
signal we're looking for. 
So here is an image which is from the 
boomerang measurement, it's a false color 
representation of temperature 
fluctuations in the sky. 
And you can see that they're 
characteristic size blobs, they turn out 
to be about 1 degree. 
So that is actually size of the particle 
horizon at the time of the coupling. 
So here again is how this works, in the 
early universe there will be density 
fluctuations as residual of quantum 
processes. 
Matter will be falling toward the densest 
parts, radiation will follow and have 
slight Doppler shifts, this is why things 
are called Doppler peaks later. 
And when the coupling time comes the 
pattern is frozen. 
If you now remember Fourier decomposition 
and in density field. 
In any number of dimensions, whether it's 
a straight line, like normal acoustic 
signals, or three dimensional field and 
density, can be decomposed into set of 
overlapping waves. 
And the largest one of those, is the 
largest wave of them that can be 
accomodated, which is the size of the 
particle horizon. 
The pattern will then stay imprinted, on 
the micro background radiation. 
After it's been decoupled from the 
matter, and by measuring it we can infer 
things about size of the horizon, and 
expansion rate at the time it was 
released, and it depends actually in all 
manner of cosmological parameters, which 
can be computed nicely from theory. 
The way we quantify this is through 
spherical harmonics, which is essentially 
in equivalent of Fourier decomposition on 
a sphere, schematically this is how it 
works, just like in Fourier analysis, 
fluctuations of certain size would be 
represented as a, peak in the power 
spectrum, for responding to that spatial 
wavelength. 
The big ones, would have, very low 
spatial frequency. 
The small ones would have very high 
spatial frequency. 
Here is a simple mathematical, simulation 
of this from N. 
Wright. 
Putting different numbers of waves on a 
sphere, corresponding to a different wave 
number, which is called l. 
Mathematically, this is, again, 
equivalent to Fourier decomposition, but 
on a sphere. 
And instead of fewer components, we are 
talking about spherical harmonics and any 
signal on the surface of the sphere can 
be expressed as a sum of spherical 
harmonics weighted properly component by 
component and formulas for each one of 
those exist and can be it computed. 
So what's measured, really, is a 
combination, of many different waves, but 
different wavelengths, on the sphere, 
have different weights. 
And, their distribution will be the power 
spectrum. 
So again, this was completely equivalent 
to power spectra in, Fourier analysis, 
except that now their waves are in a 
sphere, and no a line, or, in a plane. 
So from the measurements we can infer 
what the power spectrum is and from that 
we can then infer something about initial 
density fluctuations. 
he characteristic size that corresponds 
to particle horizon of the time is given 
by the wave number is equal approximately 
180 degrees divided by that Spherical 
harmonic l and if we can find out what 
that is then we can say something about 
size and expansion rate of the unaries at 
that time.So here WMAP results, interim 
results they got a slightly better later 
as they kept reducing delay time and 
there is a very prominent and obvious 
peak at about. 
L of 200, or angular scale a little less 
than one degree, and that corresponds to 
the size of the horizon. 
The other bumps you see are harmonics of 
the base frequency. 
So different cosmological models in 
different combinations of parameters Make 
a prediction of a pair that will go 
through these data points and shown here 
is a particularly well fitting model that 
is model that's now pretty much generally 
accepted. 
The exact positions and amplitudes and 
relative amplitudes and widths of these 
peaks depend. 
Again, on complicated mi-, mixtures of 
cosmological parameters. 
Total matter density, dark energy 
density, baryonic density, expansion 
rate, and so on. 
And in principle could be used to 
constrain all of it. 
However this is a very complex process 
and analysis involves creating large 
ensembles of Model universes and finding 
out which fit best and what are, what are 
the likelihood distributions of each 1 of 
the parameters So the 1st question was, 
what is the basic geometry of the 
universe? Is it open, closed or just 
critical? And in fact. 
It turns out it was flat within the 
measurement errors. 
That initial measurement, so that omega 
total is within 1 sigma away from unity. 
So even the original measurement implied 
that universe is flat within measurement 
errors, which are of the order of a 
couple percent. 
Since then, this got even more precise. 
That in itself is a very important 
result. 
The universe is spacially flat. 
But remember, it, that can be achieved as 
a many different combinations of the 
density of matter and density of, 
dark energy or cosmological constant. 
So by itself this measurement doesn't 
tell you much about the dark energy. 
But combined with others it can be used 
as a very powerful constraint. 
So, for example, if we can deduce from 
dynamical measurements that the Ω of 
mater is about 0.3 then this immediately 
implies that Ω of the dark energy is but 
0.7. 
Or if we can combine it with another 
measurement, like that one of supernovi. 
That will do the same thing. 
It's important to note that since so many 
parameters are mixed together in 
producing these patterns of density 
fluctuations. 
There's some degeneracy 
which means essentially that lot of them 
will be coupled together and in this 
particular case error ellipses are highly 
elongated along the line that's almost 
parallel to the flat universe line in the 
old diagram of omega matter versus omega 
vacuum. 
Which is why we think the universe is 
very close to flat so that degeneracy can 
be broken by a different measurement 
which would have error ellipses that are 
not oriented in the same way and you may 
recall that those from supernova 
measurements looked pretty much 
orthogonal through this. 
Another important measurement comes out 
of this, 
is how many baryons are there in the 
universe? The more matter there is, 
stronger fluctuations, and therefore the 
amplitudes of the peaks will be higher. 
So here are examples of 2 models with, 
different amounts of Baryonic matter. 
And by fitting to the actual data we can 
infer omega baryons. And the result is 
shown here, expressed in units of h which 
is Hubble constant units of 100 
kilometers per second per mega-parsec 
since we know h is roughly point 7, then 
this really means the mega-variance is 
about 4.5%. 
And this is in remarkably good agreement. 
With a measurement from cosmic 
nucleosynthesis, that we will come to 
later, which is, completely independent, 
assumes different physics, different 
measurements and different everything, 
which is why we believe that this result 
is probably correct, because when you 
have different. 
Matters leading to the same, result, 
then, that gives us, much more credence. 
So the question then arises, alright if 
there were these characteristic 
fluctuations, at the time of the 
coupling, will the be observable later 
on? And the answer is yes. 
There will be, corresponding imprint, on 
a very large scale structure in the 
universe. 
Which could be observable in principle in 
clustering of galaxies at comparable 
scales which are roughly hundred twenty 
mega par secs for the age of one for two 
hundred mega par secs for realistic 
values of Hubble constant. 
Hints of these were seen first, Redshift 
survey from Australia, the 2DF, redshift 
survey which we'll address later. 
And then confirmed, with Sloan Digital 
Sky Survey, there is a slight excess of 
power in clustering of galaxies on the 
scales that correspond now to that first 
Doppler The peak, except this is much 
later in the history of the universe. 
So the same standard ruler is now 
observed at different redshifts, and that 
makes the test far more powerful. 
Essentially, what that means is the error 
ellipses now rotate, and from multiple 
measurements, you can deduce A lot about, 
geometry, even without re, resorts, to 
the other measurements like supernovae. 
Now there are, many efforts, aimed to do 
precisely this. 
To observe the slight excess of 
clustering, corresponding to the first 
Doppler peak in microwave background, at 
the range of redshifts. 
And that can constrain cosmological 
perameters even better. 
Here is a table, from some of the 
cosmological parameters, many of which we 
haven't introduced yet, having to do with 
structure formation. 
Just as an illustration of the precision, 
that was obtained from WMAP. 
It actually got even better. 
this was after 3 years, of data. 
And now we have final results that after 
9 years of data which is very slightly 
different and more precise even better 
data are coming. 
ESA has a satellite called plank which is 
essentially like WMAP with even a higher 
precision, and we expect to see results 
from that within a year or thereabouts. 
Next time, we will address source counts 
as a cosmological test