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Finally, in our census of the contents of 
the universe we come to the one that's 

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the greatest mystery of them all, the 
dark energy. 

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I can pretty much condense this lecture 
into two words, nobody knows but let's 

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elaborate little bit. 
Just to remind you various cosmological 

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tests implied at about 70%, of the 
critical density of the universe is made 

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out of this mysterious component. 
Its effects are to accelerate the 

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expansion of the universe. 
This affects the age of the universe, and 

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therefore may also affect the growth of 
density perturbations, that give rise to 

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the large scale structure. 
It is an effect that's only apparent at 

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large cosmological distances which 
explains why it hasn't been seen earlier. 

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And it's certainly an outstanding puzzle, 
and not for the lack of trying. 

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As you'll see later, many people have 
tried. 

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So sometimes we talk about cosmological 
constant, which is just one possible 

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form. 
A more general form of dark-energy is 

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called quintessence, I'll define that in 
a moment. 

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The plot on this slide, shows succession 
of propability contures, for what the 

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values of density parameters of matter in 
vacuum, which is dark energy could be, as 

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a succession of different experimental 
constraints. 

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As you can see, they condense to the 
value that we always quote for a, for the 

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concurrence cosmology. 
Again, to remind you the classical origin 

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of the cosmological constant was 
essentially, as an integration constant, 

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in Einstein equations. 
It simply comes out the general theory 

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for relativity, but the theory does not 
specify its value. 

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For that matter, the theory doesn't 
specify value of the Newton's 

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gravitational constant either. 
And you could think of that as a new 

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constant of nature, whose value is 
something at which is probably determined 

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observationally. 
Since energy density implied by 

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cosmological constant is constant in 
time, it responds roughly to the force 

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that is proportional to the distance, 
like the elastic force. 

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You can think of it as the elasticity of 
the physical vacumn, although in this 

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case it actually is the spring that 
experls. 

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The sine convention is such, that 
positive value of cosmological constant, 

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which contributes to the positive mass 
energy density, is a repulsive force. 

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The first attempt to really understand 
physically what's going on, was due to 

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the Great Soviet astrophysicist, 
cosmologist Yakov Zeldovich. 

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As early as 1967, he proposed that this 
must be related to physical properties of 

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the physical vacuum. 
Now in Einstein's days vacuum was vacuum, 

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but the quantum physics told us that 
vacuum is very much alive. 

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It's filled with virtual particles and 
anti-particles. 

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It's form and annihilate on tiny scales 
that are consistent with uncertainty 

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relationship. 
The existence of these virtual particles 

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has actually been experimentally 
confirmed in an indirect sense through a 

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thing called The Casimir Effect and also 
through some subtle effects of quantum 

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field here. 
So you can think if cosmological constant 

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or dark energy as the ground state of the 
physical vacuum of the entire universe. 

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Now you may also recall from your quantum 
physics that if we know that something is 

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the ground state we cannot tell what the 
value of that is and if the universe is 

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in some higher energy level state it can 
decay to the lower energy state and its 

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exactly the mechanism proposed for the 
inflation. 

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So in some sense. 
Inflation is all about the cosmological 

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constant, but not the one we have today. 
If indeed dark energy is a product of 

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quantum processes and it is obviously an 
aspect of gravity, we need quantum theory 

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of gravity in order to understand it. 
We do not have such a theory yet. 

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And nevertheless people have tried. 
Now that has led into us probably the 

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single worst scientific prediction of all 
time and it goes like this. 

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Remember Planck units? Well those are 
units composed of physical constants and 

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so you can evaluate what's the Planck 
energy density. 

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It turns out number you get is 123 orders 
of magnitude higher than what's actually 

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observed. 
Well, that's a little bit of an 

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embarassment. 
Now physicist could think of ways of 

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producing such energy density but then 
you have to cancel it and it's very hard 

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to come up with a mechanism that will 
cancel it. 

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Not exactly but to 1 part into 10^123 
which is called the fine-tuning problem. 

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Now the obvious conclusion of this 
exercise is that this is a completely 

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wrong way to try to explain it. 
Nevertheless, for some reason, people 

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thought well, if it's not this it must be 
zero. 

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Which is pretty much like saying, well I 
can't tell what it is, therefore let's 

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pretend it doesn't exist. 
It wasn't a very strong argument. 

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Simply said, we don't know how to compute 
it yet. 

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Nevertheless, it was decided to ignore it 
more or less. 

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Even though observers kept saying that 
well maybe there is some evidence for it. 

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Most theories pretty much decided that it 
must be zero, until the evidence became 

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so strong that it had to be really taken 
into account. 

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So, let me make the distinction here. 
Dark energy could have many different 

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functional forms as as it counts, say the 
function of time, or distance or 

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expansion factor. 
And, if it's constant in time, if it's a 

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constant energy that's, then it is 
cosmological constant. 

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But the more general case, is the case 
where it changes in time. 

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That's called quintessence. 
And in language of the equation of state 

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it implies that little parameter w is a 
function of time. 

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So we know from observation that it's 
pretty close to constant, and may be 

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absolutely constant. 
But there is some room for its variation, 

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and if it does vary in time, that would 
be a very valuable hint for what physical 

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mechanisms might be. 
Now there is something called the 

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coincidence problem, which basically says 
that, isn't it remarkable that we live in 

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time of history's universe where the 
energy density of vacuum is comparable to 

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the one energy density of matter. 
I don't find this to be a very strong 

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argument because through most of the 
history of the universe this was the 

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case. 
Now usually, people who insist on this 

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problem plot things a logarithmic axis, 
or log of time or log of the expansion 

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factor and then you can squish this 
diagram all you want. 

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And so then it does indeed seem like this 
was a very special time where the 2 

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curves of omega matter, omega vacuum do 
cross, but this is purely an artifact of 

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plotting things in order, logarithmic 
axis. 

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If you're plotting linear time, proving 
air expansion factor, well then most of 

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the history of the universe was like 
this. 

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This doesn't remove the puzzle and indeed 
this really is an outstanding challenge 

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for theoretical physics. 
There are many different models that have 

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been proposed. 
There are probably thousands, literally 

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thousands of papers trying to explain it 
but most of them fall in one of the 

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several categories. 
Many assumed that there is some sort of 

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quantum field that decays just like 
happening in inflation, so this would be 

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the 2nd inflation. 
The physical origin of this field is 

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completely unknown and it's very much ad 
hoc. 

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It was invented just to make cosmological 
constant today. 

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Another approach is to modify theories of 
gravity. 

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In a more serious fashion than say, 
[INAUDIBLE] does not completely 

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consistent with theory of relativity. 
And there are models that predict that. 

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There is a very interesting class of 
models called holographic theories. 

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And they're essentially related to value 
of vacuum energy density to the area of 

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our horizon. 
And this is part of a much deeper 

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physical understanding of the origin era 
of time and entropy. 

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But there is still not a single model 
that is universally accepted. 

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String theory Has come up with the idea 
of cosmic landscape and the idea here is 

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that there are many universes. 
Remember the multiverse from inflation, 

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ours is just one of the many universe 
bubbles inflating in a bigger, bigger 

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universe. 
That's entirely speculative of course and 

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moreover, it's apriori untestable. 
There are ways in which we can estimate 

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that the number of independent universes 
with different physics is 10^500. 

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And the idea is that physical constants 
are, are random drove and they differ 

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from universe to universe. 
And we just happen to live in one in 

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which the logical constant, as well as 
any other physical constant happen to 

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have these values. 
I do not find this terribly compelling. 

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Because it's purely adhoc and it's also a 
Purian testable and one of the important 

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characteristics of science is that it has 
to be testable. 

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There are also models that connect dark 
energy and dark matter and so on and so 

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forth. 
But the fact that we have thousands of 

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them tells you that we don't have a 
single one that's any good. 

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So one possible path forward is to find 
out if the, vacuum energy density changes 

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in time. 
And there are many experiments and 

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surveys currently designed to try to 
measure precisely that. 

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So far all the results are consistent 
with Truly a constant energy density. 

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Here again are some of the observational 
results. 

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These are, again, probability contours. 
This time in the plane that shows 

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equations state parameter W which you may 
recall is exactly minus 1 for the case of 

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cosmological constant plotted against 
other cosmological parameters Will make 

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it matter and different observational 
constraints overlap, condensing 

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probability contours. 
So maybe this measurement is not to 1% 

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level but it's maybe 10% level right now 
but they're always consistent with the 

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case of cosmological constant. 
Still, some, variation in times locked, 

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and better experiments will confine this, 
even further. 

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This is a slight different version of the 
plot, this time w is plotted against the 

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energy density of the vacuum itself. 
And again, error ellipses overlap and all 

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zoom in onto the region where vacuum 
energy density is about 73%. 

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And W is exactly minus one but the case 
is still opened. 

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So there you have it, it's still a 
mystery, it's a wonderful physical 

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problem hopefully someday we'll all 
actually solve it but the recap this is 

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what we know about the composition of the 
universe it's overall energy matter 

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density is close to the critical to 
within measurement errors of about 1 or 

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2%, and maybe absolutely equal to it. 
Off that, about 73, 74% is in the form of 

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dark energy the rest in the form of 
matter. 

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Off that only 4.5% or so is in the form 
of Bariums and the rest is in some as yet 

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unknown form of non-bariomic matter. 
And among the bariums only have half of a 

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percent is in the form of visible stars 
and the rest of it is probably hot gas. 

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So, it's quite remarkable that all of the 
universe that we actually do see is only 

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half of percent of its total matter 
energy density content. 

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Next week, we'll talk about structure 
formation in the universe.