So, by the 1970s, say, after the discovery of the cosmic microwave
background, the successes of Big Bang nucleosynthesis, doubts about whether the
Big Bang was a real event had pretty much been dispelled.
but the idea that we could actually make precission measurements of the
cosmological parameters seemed far fetched.
So, people played around with models, mostly based on their theoretical biases.
the situation has changed drastically, the past few decades.
And the first precision measurements of cosmological parameters were made by
measuring the anisotropy of the cosmological microwave background.
Remember, that in the 1990's, the COBE satillite produced the first
anisotropy detected the motion of Earth through the cosmic microwave background.
Subtracting that, you see that even absent Earth's motion, this is sort of
taking into account Earth's motion, the microwave sky is not completely
isotropic. This, remember, is the structure of the
universe, this is telling us something about the way the universe was when it
was 380,000 years old. This is the oldest light we're able to
see. These are, if you want, the, a pattern of
some inhomogenieties in the universe which hopefully later lead to the
production of galaxies and clusters, and so on.
Because the universe today is certainly not homogeneous.
This was very exciting. We could learn a lot from it.
In fact, a follow-up mission later renamed the Wilkinson Microwave
Anisotropy Probe was launched and you can see that WMAP produced a far more
detailed image of the sky. And what is it that we learned from these pictures?
We see regions that are hotter and regions that are colder.
What is it that we learn from this? Well, the first thing is again analysis
of essentially the spectrum of, of fluctuations as a function of angular
variation. So, over what angular ranges do does the,
the temperature of the microwave background, what that maps is the effect
of temperature, so there are regions of slightly hotter and slightly cooler.
And the what we see is that large at angles above about a degree, there is
very little correlative fluctuations, no large splotches are there in the galaxy.
Of course, in the middle, that in the way. But at a range, at an angular size
of about a degree, there is a large amount of fluctuation.
And then, at about a third of a degree, and again at about a quarter of a degree,
and to the less extent that about a tenth of a degree,
there are smaller peaks. But, the, let's focus for a moment on this main peak,
which is the dominant peak the dominant size of angular features of the microwave
background as a degree. What does that tell me? Well, what is
this? These are the images I claim of density, or sound waves in that
primordial plasma at the age of 380,000 years after the Big Bang.
how does this work? Well, you'd expect that there could be sound waves in the
plasma, some region at by fluctuation becomes dense.
It becomes hotter because of the compression.
The heat generates radiation pressure that expands the region again, and you
get this sort of oscillatory wave behavior.
Two things to take into account. One is, all of this is dominated, these
are, this plasma has gravitationally interacting.
And it's responding to the gravitational pull of the much larger concentration of
dark matter that is around. And the other thing is,
that in fact, denser regions show up as colder in this map of the sky.
The reason is indeed they were a little bit warmer, but this is overshadowed by
something called the Sachs-Wolfe effect. Denser regions are deeper gravitational
wells. The gravitational red shift of the
photons emerging from these denser regions is larger than that from less
dense regions. This overwhems the actual heating of the
local region. So, in fact, the colder regions in the
microwave sky represent denser regions. But, be that as it may, we are mapping
essentially the density or temperature fluctuations of the universe at 380,000
years and we're mapping these sound waves.
Now, what do you expect the wavelength of these sound waves to be? Well, it turns
out that we have a very good prediction for what the typical wavelength of such a
sound wave would be. the typical wavelength, it turns out, is
of the order of the distance sound can travel in that plasma in the time 380,000
years that the universe has existed. Certainly, waves with wavelength larger
than this should not exist because the wavelength basically, the, the size of a
peak, a region that then coherently fluctuate to higher density without
dissipating should be limited, just as we have in the past used the speed of light.
Here, we're using the speed of sound to say that different regions can
communicate with each other by the speed of sound.
And this means that that wavelengths that you can expect should be smaller than or
equal to, so smaller than or equal to the distance that sound could have traveled
by that time in the age of the universe. Now, the speed of sound in this dense
plasma is very high. It's 1 over square root.
of 3 times the speed of light, because of the properties of strongly interacting
plasma. And since we know the, distance that light could have traveled by this
time, that is, the horizon distance wherein a matter dominated universe,
we've we're talking about 380,000 years so it's after the 55,000 year radiation
to matter domination. The horizon distance at time t,
the distance light would have traveled since the big bang is 3*c*t.
Since sound travels the square root of 3 1 over the squared of 3 times the speed
of light, the wavelength we expect is 1 over square
root of 3 times this, or this is our wave length.
You can plug in the numbers, we know that time, 380,000 years.
It turns out that we're talking about a wave length of about 201 kiloparsec.
So, these are pretty long wave length oscillations in the plasma.
Now, we are looking at this at a coordinate distance, this happened at
some place. And the coordinate distance that light travels in the time from this
time to our time. You can compute that using our understanding of the expansion
of the universe. the distance time travels between t
ionization and t0 is given by this expression it's this one third power.
you can recognize at least that if I set t ionization to zero, the time that light
has traveled since the Big Bang in this dust dominated universe is 3ct during
this calculation requires an integral so I won't drag you through it.
But, since we know that a(t) during the dust domainted era is given by
a0*t/t0^2/3, I can replace t ionization over t0.
And a0 is 1 by ionization to the 1/2 because I substitute to the power 1/3, to
the power 3/2 to get 1/2. So, I get this expression for the
coordinate distance. What is that? That is the distance today
of the place from which we are seeing the cosmic microwave background.
You can evaluate this and we will later find the number.
But, for now, I want the expression. so what does this tell me? Well, what
does this predict about? I have the wavelength.
I have the distance. I want to predict the angular size in the
sky, small angle formula.
Let's use the small angle formula. I'm going to use the small angular
formula, angle formula assuming the universe is
flat, remembering that the angular size distance is coordinate distance, distance
to date, divided by 1+z or multiplied by the scale factor.
So, I plug in what I had. The coordinate distance is this. The ang, the wavelength
is this. I, the redshift, 1 plus the redshift is
the inverse of the scale factor. I evaluate this.
The scale factor at ionization is 1100, plugin, you get 1 degree.
So, what I have is that if I remember to apply the geometry of Friedmann, Roberts,
and Walker and I assume that space is flat, I predict the correct angular size
for these accoustic waves in the plasma. In other words, we have just proved the
space is flat because remember what I used essentially in the small angle
formula is the idea that geodesics are straight lines and triangles behave as
they should. If the world, universe for example, had
negative curvature, then the small angle formula would be ruined.
Theta, as observed, would be smaller than a degree that you would predict from the
flat universe for a given size. Whereas if the universe were positively
curved, I would observe a large angle corresponding to the same triangle.
And so, the fact that we obtain agreement is very strong evidence that space is
flat. Here's this rather undramatic, because
realistic representation of the triangle in a negatively curved.
Or as they call it, open universe. And you would predict a smaller angle
than the angle that we found. And so, when I said that I know that the
universe is rather precisely flat, I have managed to draw a actual triangle
whose base I know from other consideration, whose length I know from
other consideration, compare to the small angle formula.
And I have measured the curvature over a distance of about 16 billion light years.
That's a pretty good base. So, I am constraining the curvature to be
almost precisely zero. This is why we know space is flat.
There is more structure obviously than just the first peak, there are these
subsequent peaks at smaller angular distributions.
First of all, there's the total absence of any fluctuations larger than a degree.
This makes sense. We said fluctuations larger than this
could not have formed because distinct regions within the same wave were outside
each others particle horizon, could not have gotten together a coherent wave.
understanding the subsequent peaks, you have to take into account, as I said,
that the sound is sort of controlled by the density fluctuations of the dark
matter. it turns out that the height and position
of the second peak are sensitive to the baryonic dust density.
The third peak, relative to the second peak, it's height and position are
sensitive to the density of dark matter, that's a little bit technical for what
we're doing. But, by combining observations of all the spectrum, we can
learn information both about the total density, remember we have discovered that
the universe is flat. So, omega is essentially one.
a combi, that, that explains why I am so confident that omega, dark matter plus
dark energy normal matter adds up to one plus radiation which is very small.
And furthermore the ratio between dark matter and baryonic densities is further
constrained by this measurement together with nuclear nucleosynthesis, we are
beginning to get a handle on the precise values of these parameters.
Lots more information can be extracted from this cosmic microwave background and
is being extracted and more is constantly being done, polarization data analysis of
the interaction of the background radiation with galaxy clusters.
there is a lot of information and you can got to the WMAP project webpage and learn
what else we can learn from.