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.