What I'd like to do now, is say a bit more
about dark matter and dark energy, and
how we infer their existence and
properties from observations in cosmology.
And this all starts with
Friedmann's equation.
As I told you,
he was the first to understand
the full dynamics of
the expanding universe.
And what he found was that those
dynamics are the same as familiar systems.
So for example,
let me take this pen and throw it up.
Initially, it moves quickly,
then it moves slowly.
Its kinetic energy is reducing but
its total energy is conserved.
So it transforms kinetic
energy into potential energy.
Thus.
We can say kinetic plus potential
is a constant, total energy.
Friedmann's equation for the whole
universe, has no more content than that.
So, if you'll forgive me,
because astronomers really love equations.
I'm going to write it down
just to convince you that
it really is quite a simple
thing to deal with.
And if you're not mathematical then,
all I'm doing is writing
this in other language.
What I need is to symbolize R of t,
by which I mean the size of the universe.
I won't be specific about
precisely what that means.
The kinetic term corresponds to how
fast the universe is getting bigger.
So in calculus notation,
that's dR by dt, but it
just means a kind of speed for
the whole universe. And square it.
Then something that involves
the gravitational constant.
The density.
Of the whole universe,
times a scale factor
squared divided by 3,
is equal to a constant.
And this constant, according to general
relativity comes from the curvature.
So, Friedmann's equation involves
the rate of expansion of the universe,
the density of what's in it and
the curvature.
So, K would be 0 for
a flat universe, as it seems to be.
So, what that means, is we can observe
how the universe expands over time.
This can tell us two great things.
It can tell us the density of
the universe as a function of time.
And it can tell is whether
the universe is curved.
So that sounds almost too good to be true.
The question is how do we
figure out how the size of
the universe changes with time?
So, how do we measure the expansion
history of the universe?
One way of looking at this is
to go back to Hubble's Law.
And say that we need
the hubble constant as
a function of time, because that
governs the rate of expansion
of the universe, which is what we need.
That means, since we can observe
spectroscopic red shifts,
we just need some means of inferring
the distance to objects seen at
great light travel times.
Measuring distances in cosmology is,
is a real challenge,
because everything is so far away.
The standard technique
is known under the strange name
of Standard Candles.
Imagine you had a very powerful light
bulb that you knew was of uniform output.
If it's nearby, it's very intense.
As you take it further away,
this intensity would fade
so that the relative intensity
that you observe is a 
direct guide to the distance.
In fact, you would say that the,
the flux of light,
symbolized by F, it's just proportional
to 1 over the distance squared,
if you can astronomical objects that
all emit the same amount of energy.
A very good candidate for
these emerged during the 1990s,
Supernovae, SNE for short.
Which are exploding stars
around one cell of mass,
in the case of type IA. And
these all empirically have very
nearly the same energy output.
So we can use them to measure distances.
And therefore empirically one can map
out the relationship between distance
and red shift in cosmology, normally
symbolized 'z', but this just means the
small distances ... the recessional
velocity in units of the speed of light.
Hubble's Law says this is linear.
But at large distances,
this has some curvature.
And it's the curvature of this relation
that represents the change of H with t.
And this is what lets us
measure how the universe has
changed its expansion over history.
The conclusion is that you can
only match the data that we
have with Friedmann's equation
if the density of the universe consists
of a number of different ingredients.
There has to be about 70% dark energy.
And dark energy remember is
something that doesn't change in
its density with time,
and about 30% matter.
But this in itself is broken
into about 25% dark matter,
and about 5% of ordinary matter,
atomic matter.
This is the 5% that we got from
nuclear reactions. So, strangely,
the total adds up to approximately
omega equals one.
And therefore, the universe is flat.
But most of its contents are not
the ordinary atomic material that we see.
So the expansion history from supernovae
is one powerful piece of evidence for
an accelerating universe.
Another way we can learn about this, and
to learn more about
the existence of dark matter,
comes from studying
structure in the universe.
And what I mean by this, is looking at
the distribution of the building blocks of
the universe, that is the galaxies.
Which you want to do in three dimensions.
We do this very simply
just using Hubble's Law.
So we measure the velocity,
that gives us a radial distance.
So we can immediately take a set
of galaxies observed on the sky,
and figure out how far
away each one of them is.
So that means take a picture of the sky,
take say some,
narrow strip on it, and now expand this in
the radial direction using Hubble's law.
What this allows you to do, is then
cut out a kind of pizza slice out of
the universe,
where this is the radius D and
the galaxies are spread out in
distance and in direction on the sky.
Now what we find is that there
are patterns in this distribution.
Colossal patterns.
The galaxies tend to make up chains,
filaments of galaxies, connected together,
surrounded by voids,
where there's very few galaxies.
These patterns are exquisite,
and these structures are huge.
They might be 100 million
light years across.
They must be some relic from
an early phase of the universe.
Which tells us a great deal about how
the universe got to be the way it is.
But for the moment, what I'm interested
in is using these patterns as a way of
diagnosing the presence of dark matter.
So where does the structure from?
In part, the answer is gravity.
Wherever there's more matter than average,
it will suck further matter in, and
computer simulations of this process, give
us images that look very like the galaxies surveys.
So we know gravity's at work here.
Now this is useful,
because the operation of gravity has
changed over the history of the universe.
If I plot density, this is time.
In the past, the density of matter was
higher, because the universe was smaller.
Today, there's radiation, whose energy
density is much less than that of matter.
The microwave background
is almost negligible.
But it becomes more important as
we go back into the hot, big bang,
and there is a cross over time, and
this is somewhere around 100,000 years.
Before that the energy density in
the universe was dominated by radiation.
One can see the time that this occurred
in the detailed properties of the,
the fluctuations that
the galaxies obey in space.
And also, if we change
the amount of matter, make it,
less, that transition
occurs at a later time.
And so the corresponding length scale,
the speed of light times
the time would be larger.
So we find written in the sky
some information about
the matter density from the so
called large scale structure.
So by mapping the three
dimensional distribution of galaxies,
we're able to infer
the density of the universe.
And this is where the contribution of
matter that is not dark energy, because
this is only matter that can clump.
So, the fact that this is
greater than the material,
of ordinary atomic material that we
infer from say nuclear synthesis,
tells us that the majority of the
clumpable matter in the universe is of
a form that we only see through gravity,
we don't see from radiation, so
this is dark matter.
The large scale structure is probably the most
accurate way of measuring the total
amount of dark matter, but we can see
its influence much more directly.
For example, in galaxy rotation curves.
So if I have a galaxy,
like the Milky Way, stars and
gas orbit around the center.
And if you plot, this orbital velocity.
This is the radius from
the center of the galaxy.
You might expect to find
something like this.
Where the velocity declines once you
reach the edge of the visible galaxy,
and you've run out of matter.
Now, you're just further away
from what matter there is.
But the data actually tend to stay flat, so
this is the visible matter, and so
the difference is dark.
So, apparently the outskirts of
galaxies are dominated by dark matter.
And that's one of the most direct
pieces of evidence that we have for
its existence.
If a structure in the galaxy distribution
grew over time under the action of
gravity, we should be able to see that.
And this is possible using
the microwave background.
So, here we are,
observing the last scattering
surface at the time of 400 thousand years.
The seeds for the large scale
structure should be in place, already.
So, there should be regions that
the density that are higher than average.
And from these we get more
radiation than in between.
So fluctuations in the intensity of
radiation are expected on the sky.
And these were first seen 
in 1992.
And the fluctuations at
about 1 part in 100,000.
Slightly hotter, slightly colder,
all across the sky.
And these patches that we see
are about 1 degree across.
This allows us to learn something
about the curvature of the universe,
because if I observe the sky in
a closed universe, then the light
rays would tend to reconverge.
And this is just like what
would happen on the Earth.
Two people set out from
the North Pole along great circles.
By the time they come to the South Pole,
their paths have reconverged.
The curved space brings light rays
together, positively curved space.
Negatively curved space
would open them up.
Whereas a flat universe is in between,
and therefore the size of
the spots of the microwave sky
can be used to distinguish between
the closed case and the open case.
And they favour the flat case.
So, therefore, we see overall that
the total density of the universe is 1.
They already had matter
contribution of 0.3,
and so
this tells us that something else that
doesn't clump must be the vacuum
energy as about 70% of the content.
This argument was already
made in about 1990.
The interesting thing is, very few members
of the astronomical community believed it.
And it's worth asking why this was.
The answer is that to anybody be
they a scientist or not, believing that we've
proved that the energy density of the vacuum
is non-zero, is such a radical step,
that you're very reluctant to take
it with out further evidence.
But then, at the end of the 1990's
the evidence from supernova came along and
gave us the same conclusion.
Now we had two arguments that both
call for the existence of dark energy.
And so almost overnight this
became a new standard model.
The burden of evidence was so strong,
that a new paradigm was established.
