Finally, in our census of the contents of 
the universe we come to the one that's 
the greatest mystery of them all, the 
dark energy. 
I can pretty much condense this lecture 
into two words, nobody knows but let's 
elaborate little bit. 
Just to remind you various cosmological 
tests implied at about 70%, of the 
critical density of the universe is made 
out of this mysterious component. 
Its effects are to accelerate the 
expansion of the universe. 
This affects the age of the universe, and 
therefore may also affect the growth of 
density perturbations, that give rise to 
the large scale structure. 
It is an effect that's only apparent at 
large cosmological distances which 
explains why it hasn't been seen earlier. 
And it's certainly an outstanding puzzle, 
and not for the lack of trying. 
As you'll see later, many people have 
tried. 
So sometimes we talk about cosmological 
constant, which is just one possible 
form. 
A more general form of dark-energy is 
called quintessence, I'll define that in 
a moment. 
The plot on this slide, shows succession 
of propability contures, for what the 
values of density parameters of matter in 
vacuum, which is dark energy could be, as 
a succession of different experimental 
constraints. 
As you can see, they condense to the 
value that we always quote for a, for the 
concurrence cosmology. 
Again, to remind you the classical origin 
of the cosmological constant was 
essentially, as an integration constant, 
in Einstein equations. 
It simply comes out the general theory 
for relativity, but the theory does not 
specify its value. 
For that matter, the theory doesn't 
specify value of the Newton's 
gravitational constant either. 
And you could think of that as a new 
constant of nature, whose value is 
something at which is probably determined 
observationally. 
Since energy density implied by 
cosmological constant is constant in 
time, it responds roughly to the force 
that is proportional to the distance, 
like the elastic force. 
You can think of it as the elasticity of 
the physical vacumn, although in this 
case it actually is the spring that 
experls. 
The sine convention is such, that 
positive value of cosmological constant, 
which contributes to the positive mass 
energy density, is a repulsive force. 
The first attempt to really understand 
physically what's going on, was due to 
the Great Soviet astrophysicist, 
cosmologist Yakov Zeldovich. 
As early as 1967, he proposed that this 
must be related to physical properties of 
the physical vacuum. 
Now in Einstein's days vacuum was vacuum, 
but the quantum physics told us that 
vacuum is very much alive. 
It's filled with virtual particles and 
anti-particles. 
It's form and annihilate on tiny scales 
that are consistent with uncertainty 
relationship. 
The existence of these virtual particles 
has actually been experimentally 
confirmed in an indirect sense through a 
thing called The Casimir Effect and also 
through some subtle effects of quantum 
field here. 
So you can think if cosmological constant 
or dark energy as the ground state of the 
physical vacuum of the entire universe. 
Now you may also recall from your quantum 
physics that if we know that something is 
the ground state we cannot tell what the 
value of that is and if the universe is 
in some higher energy level state it can 
decay to the lower energy state and its 
exactly the mechanism proposed for the 
inflation. 
So in some sense. 
Inflation is all about the cosmological 
constant, but not the one we have today. 
If indeed dark energy is a product of 
quantum processes and it is obviously an 
aspect of gravity, we need quantum theory 
of gravity in order to understand it. 
We do not have such a theory yet. 
And nevertheless people have tried. 
Now that has led into us probably the 
single worst scientific prediction of all 
time and it goes like this. 
Remember Planck units? Well those are 
units composed of physical constants and 
so you can evaluate what's the Planck 
energy density. 
It turns out number you get is 123 orders 
of magnitude higher than what's actually 
observed. 
Well, that's a little bit of an 
embarassment. 
Now physicist could think of ways of 
producing such energy density but then 
you have to cancel it and it's very hard 
to come up with a mechanism that will 
cancel it. 
Not exactly but to 1 part into 10^123 
which is called the fine-tuning problem. 
Now the obvious conclusion of this 
exercise is that this is a completely 
wrong way to try to explain it. 
Nevertheless, for some reason, people 
thought well, if it's not this it must be 
zero. 
Which is pretty much like saying, well I 
can't tell what it is, therefore let's 
pretend it doesn't exist. 
It wasn't a very strong argument. 
Simply said, we don't know how to compute 
it yet. 
Nevertheless, it was decided to ignore it 
more or less. 
Even though observers kept saying that 
well maybe there is some evidence for it. 
Most theories pretty much decided that it 
must be zero, until the evidence became 
so strong that it had to be really taken 
into account. 
So, let me make the distinction here. 
Dark energy could have many different 
functional forms as as it counts, say the 
function of time, or distance or 
expansion factor. 
And, if it's constant in time, if it's a 
constant energy that's, then it is 
cosmological constant. 
But the more general case, is the case 
where it changes in time. 
That's called quintessence. 
And in language of the equation of state 
it implies that little parameter w is a 
function of time. 
So we know from observation that it's 
pretty close to constant, and may be 
absolutely constant. 
But there is some room for its variation, 
and if it does vary in time, that would 
be a very valuable hint for what physical 
mechanisms might be. 
Now there is something called the 
coincidence problem, which basically says 
that, isn't it remarkable that we live in 
time of history's universe where the 
energy density of vacuum is comparable to 
the one energy density of matter. 
I don't find this to be a very strong 
argument because through most of the 
history of the universe this was the 
case. 
Now usually, people who insist on this 
problem plot things a logarithmic axis, 
or log of time or log of the expansion 
factor and then you can squish this 
diagram all you want. 
And so then it does indeed seem like this 
was a very special time where the 2 
curves of omega matter, omega vacuum do 
cross, but this is purely an artifact of 
plotting things in order, logarithmic 
axis. 
If you're plotting linear time, proving 
air expansion factor, well then most of 
the history of the universe was like 
this. 
This doesn't remove the puzzle and indeed 
this really is an outstanding challenge 
for theoretical physics. 
There are many different models that have 
been proposed. 
There are probably thousands, literally 
thousands of papers trying to explain it 
but most of them fall in one of the 
several categories. 
Many assumed that there is some sort of 
quantum field that decays just like 
happening in inflation, so this would be 
the 2nd inflation. 
The physical origin of this field is 
completely unknown and it's very much ad 
hoc. 
It was invented just to make cosmological 
constant today. 
Another approach is to modify theories of 
gravity. 
In a more serious fashion than say, 
[INAUDIBLE] does not completely 
consistent with theory of relativity. 
And there are models that predict that. 
There is a very interesting class of 
models called holographic theories. 
And they're essentially related to value 
of vacuum energy density to the area of 
our horizon. 
And this is part of a much deeper 
physical understanding of the origin era 
of time and entropy. 
But there is still not a single model 
that is universally accepted. 
String theory Has come up with the idea 
of cosmic landscape and the idea here is 
that there are many universes. 
Remember the multiverse from inflation, 
ours is just one of the many universe 
bubbles inflating in a bigger, bigger 
universe. 
That's entirely speculative of course and 
moreover, it's apriori untestable. 
There are ways in which we can estimate 
that the number of independent universes 
with different physics is 10^500. 
And the idea is that physical constants 
are, are random drove and they differ 
from universe to universe. 
And we just happen to live in one in 
which the logical constant, as well as 
any other physical constant happen to 
have these values. 
I do not find this terribly compelling. 
Because it's purely adhoc and it's also a 
Purian testable and one of the important 
characteristics of science is that it has 
to be testable. 
There are also models that connect dark 
energy and dark matter and so on and so 
forth. 
But the fact that we have thousands of 
them tells you that we don't have a 
single one that's any good. 
So one possible path forward is to find 
out if the, vacuum energy density changes 
in time. 
And there are many experiments and 
surveys currently designed to try to 
measure precisely that. 
So far all the results are consistent 
with Truly a constant energy density. 
Here again are some of the observational 
results. 
These are, again, probability contours. 
This time in the plane that shows 
equations state parameter W which you may 
recall is exactly minus 1 for the case of 
cosmological constant plotted against 
other cosmological parameters Will make 
it matter and different observational 
constraints overlap, condensing 
probability contours. 
So maybe this measurement is not to 1% 
level but it's maybe 10% level right now 
but they're always consistent with the 
case of cosmological constant. 
Still, some, variation in times locked, 
and better experiments will confine this, 
even further. 
This is a slight different version of the 
plot, this time w is plotted against the 
energy density of the vacuum itself. 
And again, error ellipses overlap and all 
zoom in onto the region where vacuum 
energy density is about 73%. 
And W is exactly minus one but the case 
is still opened. 
So there you have it, it's still a 
mystery, it's a wonderful physical 
problem hopefully someday we'll all 
actually solve it but the recap this is 
what we know about the composition of the 
universe it's overall energy matter 
density is close to the critical to 
within measurement errors of about 1 or 
2%, and maybe absolutely equal to it. 
Off that, about 73, 74% is in the form of 
dark energy the rest in the form of 
matter. 
Off that only 4.5% or so is in the form 
of Bariums and the rest is in some as yet 
unknown form of non-bariomic matter. 
And among the bariums only have half of a 
percent is in the form of visible stars 
and the rest of it is probably hot gas. 
So, it's quite remarkable that all of the 
universe that we actually do see is only 
half of percent of its total matter 
energy density content. 
Next week, we'll talk about structure 
formation in the universe.