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PROFESSOR: OK, in
that case we can
jump into the early universe.
So on the opening slide
here I have a picture
of the Planck satellite,
which is a satellite that
was launched a few years
ago dedicated to measuring
the cosmic background radiation.
Cosmic background
radiation is really
our biggest clue for the
early history of the universe.
The Planck satellite is
actually the third satellite
to go up completely dedicated to
measuring the cosmic background
radiation.
The first was called COBE
and then WMAP and now Planck.
Planck is still in orbit.
It actually is finished
with its data-taking,
although it's
nowhere near finished
with the analysis of that data.
So they made one major
data release last March,
and there are still very
important pieces of their data
that I haven't looked at yet.
And we'll be talking
more about what exactly
these satellites see.
Onward.
I want to begin by talking about
the standard Big Bang, which
will in fact be the main
focus of this course.
We'll probably spend about 2/3
of the course or so talking
about the standard Big
Bang and then move on
to topics like inflation.
That actually is, I think,
a very sensible balance,
because as you'll see once we
get under studying inflation,
it's a fairly straightforward
thing once you know
the basic equations coming
out of standard cosmology.
So I think spending about
2/3 of the term or so
on the conventional cosmology
before we get to inflation
is very sensible, because that
will set up all the principles
that we'll be using
later to discuss more
advanced topics like inflation.
The conventional Big Bang
model is basically the theory
that the universe as
we know it began some
13 to 14 billion years ago.
And now we even have a
pretty precise number
to replace this 13
to 14 billion years.
This is based on
the Planck satellite
combined with a few other
pieces of information.
The number is 13.82 billion
years, plus or minus 0.05.
So it's pretty well
pinned down now,
the age of the universe
since the Big Bang.
I should add, though, I put
in the qualifier "the universe
as we know it."
What that really means is
that I want to leave it out,
because we don't really
know that the universe began
with what we call the Big Bang.
So we have a very good
picture of the Big Bang,
and we're very confident
that it happened
and that we understand
what it looked like.
But whether or not
anything came before it
is a much more open
question which I think
is really completely open.
I think we should not act like
we know that the universe began
with the Big Bang.
And in fact later at the
very end of the course when
we discuss some of the
implications of inflation
and the multiverse,
we'll see that there are
strong suggestions that the
Big Bang was perhaps not really
the beginning of
existence, but really
just the beginning of
our local universe,
often called a pocket universe.
OK.
In any case, what the
Big Bang theory tells
us is that at least our
region of the universe
13.82 billion years ago was an
extremely hot, dense, uniform
soup of particles, which in the
conventional standard Big Bang
model filled literally
all of space.
And now we certainly believe
it filled essentially all
the space that we have
access to uniformly.
Now I should point
out that this is
contrary to a popular cartoon
image of the Big Bang, which
is just plain wrong.
The cartoon image
of the Big Bang
is the image of a small egg
of highly dense matter that
then exploded and spewed
out into empty space.
That is not the scientific
picture of the Big Bang.
And the reason is not
because it's illogical.
It's hard to know what's logical
or illogical in this context.
But simply based on
what we see, if there
was a small egg that
exploded into empty space,
you would certainly
expect that today you
would see something different
if you were looking toward where
the egg was versus looking
the opposite direction.
But we don't see any
effect like that.
When we look around
the sky, the universal
looks completely uniform, on
average, in all directions
to very high degree of accuracy.
I'll talk a little bit
more precisely later.
So we don't see any sign of an
egg having happened anywhere.
Rather the Big
Bang seems to have
happened everywhere uniformly.
OK.
The Big Bang describes a
number of important things,
and we'll be talking about this
more as the course goes on.
It describes how the early
universe expanded and cooled--
and will be spending a fair
amount of time understanding
the details behind those words.
The point is that
the Big Bang really
is a very precise model based
on very simple assumptions.
You basically assume
that the early universe
was filled by a hot gas
in thermal equilibrium.
And that this gas was
expanding and being pulled back
by gravity.
And from those simple ideas
you can really calculate--
and we'll learn
how to calculate--
how fast the universe would
have been expanding at any given
instant of time, what the
temperature would have been
at any given instant of time,
what the density of matter
would have been at
any instant of time.
So all the details
really can be calculated
from some rather
simple ideas, and we'll
have fun exploring that.
The Big Bang also talks
about how the light chemical
elements formed.
And that actually
is the main topic
of Steve Weinberg's book
"The First Three Minutes."
Because that was more or less
the time period during which
the chemical elements formed.
It turns out that most of
the elements in the universe
did not form in the Big
Bang, but formed much later
in the interior of stars.
And those elements are
then strewn out into space
in supernova explosions and
collected into later generation
stars, of which our
sun would be one.
So the stuff that we're made
out of was actually not produced
in the Big Bang, but
rather was produced
in the interior of some distant
star that exploded long ago.
And maybe many
stars, whose material
collected to form
our solar system.
Nonetheless, most of the matter
in the universe-- as opposed
to most of the different
kinds of elements--
did form in the Big Bang.
Most of the matter
in the universe
is just hydrogen and helium.
About five different isotopes
of hydrogen, helium, and lithium
were primarily formed
in the Big Bang,
and because we do have this
detailed picture of the Big
Bang that we'll
be learning about,
it's possible to
actually calculate
the predicted abundances of
those different isotopes.
And the predictions agree very
well with the observations.
And this is certainly one
of the major confirmations
we have that this picture
of the Big Bang is correct.
We can predict what the
abundance of helium-3
should be, and we measure
it, and it agrees.
It's rather marvelous.
Finally-- and this
subject we're not
going to talk about
much because it
goes beyond the
level of complexity
that the course
is going to have--
but finally the Big
Bang does discuss
how the matter ultimately
congealed to form stars,
galaxies, clusters of galaxies.
We'll talk about
that a little bit,
but we won't really
follow that very far.
That is still in principle
a work in progress.
People do not understand
everything about galaxies.
But the general picture
of that-- it started out
with an almost uniform
universe, and then
the lumps congealed to form the
galaxies and the structures--
we say certainly seems
to be a working picture.
And one can understand
a lot about the universe
from this very simple picture.
OK what I want to
talk about next
is what the conventional
Big Bang theory does not
talk about, where new ideas
like inflation come in.
First of all, the
conventional Big Bang theory
does not say anything about
what caused the expansion.
It really is only a theory
of the aftermath of a bang.
In the scientific
version of the Big Bang,
the universe starts with
everything already expanding
with no explanation of how
that expansion started.
That's not part of
the Big Bang theory.
So the scientific version
of the Big Bang theory
is not really a
theory of a bang.
It's really the theory of
the aftermath of a bang.
In addition, and maybe
in a similar vein,
the conventional
Big Bang theory says
nothing about where all
the matter came from.
The theory really assumes that
for every particle that we
see in the universe
today, there was
at the very beginning at
least some precursor particle,
if not the same particle,
with no explanation of where
all those particles came from.
In short, what I like to say is
that the Big Bang says nothing
about what banged,
why it banged,
or what happened
before it banged.
It really has no
bang in the Big Bang.
It's a bangless theory,
despite its name.
Inflation, it turns out,
fills in possible answers,
very plausible answers, for
many of these questions.
And that's what I'll
be talking about mainly
for the rest of today.
And as I said, in
terms of the course,
it's where we'll be aiming
to get about 2/3 of the way
through the semester.
What is cosmic inflation?
It's basically a
minor modification,
in terms of the overall
scheme of things,
of the standard Big Bang theory.
And the best word to describe
it is a word that I think
was invented by
Hollywood-- inflation
is a prequel to the
conventional Big Bang theory.
It's a short description
of what happened before,
immediately before,
the Big Bang.
So inflation really
is an explanation
of the bang of the
Big Bang in the sense
that it does provide a
theory of the propulsion that
drove the universe into this
humongous episode of expansion
which we call the Big Bang.
And it does it in
terms of something
that I like to think of
as a miracle of physics.
When I use the word "miracle"
in this context-- referring
to a miracle in the
scientific sense--
simply something that's
so surprising that I think
it merits being called a miracle
even though it's something
that's a part of
the laws of physics.
There are just a few features
of the laws of physics
that are actually
crucial to inflation--
I'll be talking
about two of them--
which I consider miracles
simply because-- well,
mainly because when I
was an undergrad nobody
talked about them at all.
They were just not
part of physics then,
even though they really were.
They just weren't
parts of physics people
noticed and talked about.
So the miracle of physics
I'm talking about here
is something which
actually is known
since the time of Einstein's
general relativity--
that gravity is not
always attractive.
Gravity can act repulsively.
And Einstein introduced
this in 1916, I guess,
in the form of what he called
his cosmological constant.
And the original
motivation of modifying
the equations of general
relativity to allow this
was because Einstein thought
that the universe was static.
And he realized that
ordinary gravity
would cause the universe to
collapse if it were static.
It couldn't remain static.
So he introduced this
cosmological constant term
to balance the overall
attraction of ordinary gravity
to be able to build a static
model of the universe.
As you'll soon be learning,
that's dead wrong.
That's not what the
universe looks like at all.
But the fact that
general relativity
can support this
gravitation repulsion, still
being consistent with
all the principles
that general relativity
incorporates,
is the important
thing which Einstein
himself did discover
in this context.
And inflation takes advantage
of this possibility,
within the context of
general relativity,
to let gravity be the
repulsive force that
drove the universe into
the period of expansion
that we call the Big Bang.
And in fact when one
combines general relativity
with conventional ideas
now in particle physics,
there really is a
pretty clear indication,
I should say-- not quite a
prediction-- but a pretty clear
indication that at very
high energy densities,
one expects to find states of
matter which literally turn
gravity on its head and cause
gravity to become repulsive.
In terms of the details which
we'll be learning about more
later, what it takes to
produce gravitational repulsion
is a negative pressure.
According to general
relativity, it turns out--
and we'll be talking more about
this later-- both pressures
and energy densities can
produce gravitational fields.
Unlike Newtonian physics,
where it's only mass densities
that produce
gravitational fields.
And the positive
pressure produces
an attractive
gravitational field,
which is what you would
probably guess if somebody just
asked you to guess.
Positive pressures are
sort of normal pressures,
and attractive gravity
is normal gravity.
So normal pressures
produce normal gravity.
But it is possible to
have negative pressures,
and negative pressures
produce repulsive gravity.
That's the secret of what
makes inflation possible.
So inflation proposes that
at least a small patch
of this repulsive
gravity material
existed in the early universe.
We don't really
know exactly when
in the history of the
universe inflation happened,
which is another way of
saying we don't know exactly
at what energy scale
inflation happened.
But a very logical,
plausible choice--
I don't know if logical is
the right word, but plausible
is a good word--
very plausible choice
for when inflation
might have happened,
would be when the energy
scales of the universe where
at the scale of grand
unified theories.
Grand unified theories-- we'll
talk about a little bit later--
are theories which
unify the weak, strong,
and electromagnetic
interactions into
a single unified interaction.
And that unification occurs at
a typical energy of about 10
to the 16 GeV, where GeV,
in case you don't know,
is about the mass--
or the energy
equivalent of the
mass-- of a proton.
So we're talking
about energies that
are about 10 to the 16 times the
equivalent energy of a proton
mass.
And at those energies we
think that these states that
create repulsive gravity
are very likely to exist.
And if that happened
at that scale,
the initial patch
would only have
to be the ridiculously
small size of about 10
to the minus 28
centimeters across
to be able to lead ultimately
to the creation of everything
that we see on the vast
scale at which we see it.
The patch certainly does not
have to be the entire universe.
And it could in fact
be incredibly rare,
because one thinks that outside
of that patch essentially
nothing will happen interesting.
So we expect that the
universe that we observe today
would be entirely the
consequence of such a patch.
The gravitational
repulsion created
by this small patch of
repulsive gravity material
would be then the driving
force of the Big Bang,
and it would cause the region to
undergo exponential expansion.
And by exponential expansion,
as you probably know,
it means that there's a
certain doubling time,
and if you wait the same amount
of time it doubles again.
If you wait the same amount
of time, it doubles again.
And because these doublings
build up so dramatically,
it doesn't take very much time
to build the whole universe.
In about 100 doublings,
this tiny patch
of 10 to the minus
28 centimeters
can become large enough
not to be the universe,
but to be a small marble
size region, which will then
ultimately become
the observed universe
as it continues to coast
outward after inflation ends.
So the doubling time
would be incredibly small
if this was all happening
at the grand unified theory
set of numbers-- 10 to the
minus 37 seconds, which
is pretty fast.
The patch would
expand exponentially
by at least a factor of about 10
to the 28, which as I mentioned
takes only about 100
doublings, and could
expand to be much more.
There's no cut off there.
If there's more
expansion than we
need to produce our
universe, it just
means that the patch of
universe that we're living in
is larger than we see.
But that's OK.
Everything that we see looks
uniform as far as we can see,
and how much there is
beyond that we really just
have no way of knowing.
So larger amounts
of inflation are
perfectly consistent
with what we see.
The amount of time it would
take would only be about 10
to the minus 35 seconds,
which is just 100 times 10
to the minus 37 if you can do
that complicated arithmetic
in your head.
And the region that's destined
to become our presently
observed universe at
the end of inflation
would have been only about the
size of a marble-- about one
centimeter or so across.
Now what ends
inflation is the fact
that this repulsive gravity
material is unstable.
So it decays, using the
word decay in the same sense
that a radioactive
substance decays.
It doesn't necessarily
mean exactly
that it rots like
an apple decays,
but it means that it turns
into other kinds of material.
And in particular, it
turned into material
which is no longer
gravitationally repulsive.
So the gravitational repulsion
ends, and in fact the particles
produced by this
energy that's released
at the end of inflation
become the hot soup
of the conventional Big Bang.
And this is where
the prequel ends,
and the main feature begins--
the conventional Big Bang
theory.
The role of inflation is just
to set up the initial conditions
for the conventional
Big Bang theory.
Now there's a
little caveat here.
Inflation ends because
the material is unstable,
but it only ends
almost everywhere, not
quite everywhere.
And this is basically the
way exponentials work.
And we'll come back to this
when we talk about the late time
behavior and the idea
of eternal inflation.
This repulsive gravity
material decays,
but it decays like a radioactive
substance-- which is also
an exponential-- as a half life.
But no matter how many
half lives you wait,
there's still a tiny little bit,
a tiny fraction that remains.
And that turns out to be
important for the idea
that in many cases inflation
never completely ends.
We'll come back to that.
So I want to talk more
about what goes on
during this exponential
expansion phase.
There's a very peculiar
feature of this inflation--
this exponential
expansion driven
by repulsive gravity-- which
is that while it's happening,
the mass density
or energy density
of the inflating material-- this
repulsive gravity material--
does not decrease.
You would think that if
something doubled in radius,
it would multiply by a
factor of eight in volume.
You would think the energy
density would go down
by a factor of eight.
And that certainly happens
for ordinary particles.
It's certainly what
would happen if you
had a gas, an ordinary
gas, that you just
allowed to expand
by a factor of two
in radius-- the density would
go down by a factor of eight
with volumes of
cubes of distances.
But this peculiar repulsive
gravity material actually
expands at a constant density.
Now that sounds like it must
violate conservation of energy,
because it really does mean
that the total amount of energy
inside this expanding
volume is increasing.
The energy per volume
is remaining constant,
and the volume is getting
bigger and bigger exponentially.
So the claim is that I've not
gone crazy, that this actually
is consistent with the laws
of physics as we know them.
And that it is consistent
with conservation of energy.
Conservation of energy really is
a sacred principle of physics.
We don't know of anything
in nature that violates this
principle of
conservation of energy,
that energy ultimately cannot
be either made or destroyed,
that the total amount of
energy is basically fixed.
So it sounds like there's
a contradiction here.
How do we get out of it?
What's the resolution?
Well, this requires my
second miracle of physics.
Energy-- it really
is exactly conserved.
I'm not going to tell you
about any miracles which
changed that.
But the catch here is
that energies are not
necessarily positive.
There are things that
have negative energies.
And in particular, the
gravitational field
has a negative energy.
This statement by the way is
true both in Newtonian physics
and in general relativity.
We'll prove it later.
I might just say
quickly if some of you
have learned in an E&M course
how to talk about and calculate
the energy density of an
electrostatic field-- probably
many of you have,
maybe all of you
have-- the energy density
of an electrostatic field
is a constant times the square
of the electric field strength.
And you can prove that
energy is exactly the energy
that you need to
put into a system
to create an electric field
of a given configuration.
If you think about
Newton's law of gravity
and compare it
with Coulomb's law,
you realize that it
really is the same law,
except they have a different
constant in front of them.
They're both inverse
square laws in proportion
to the two charges, where
in the case of gravity
it's the masses that
play the role of charges.
But they have opposite signs.
Two positive charges, as we
all know we tell each other,
two positive masses
attract each other.
So in fact the
very same argument
which allows you to calculate
the energy density of a Coulomb
field can allow you to
calculate the energy
density of a Newtonian
gravitational field-- still
sticking to Newtonian
physics-- and this change
in sign of the force
just carries through.
It changes the signs of all
the work that's being done,
and you get the
negative answer that
is the correct answer
for Newtonian gravity.
The energy density of a
Newtonian gravitational field
is negative.
And the same is true
in general relativity
in a more subtle way.
So what that means in terms
of conservation of energy
is that we can have more
and more matter, more
and more energy building up in
the form of ordinary matter--
which is what happens during
inflation-- as long as there's
a compensating amount
of negative energy
that's created in the
gravitational field which
is filling this ever
larger region of space.
And that's exactly what
happens in inflation.
The positive energy of this
repulsive gravity material
which is growing and
growing in volume
is precisely canceled
by the negative energy
of the gravitational field
that's filling the region.
So the total energy
does remain constant,
as it must, and there's
certainly a good possibility
that the total energy
is exactly zero.
Because everything
that we know of
is at least consistent
with the possibility
that these two
numbers are exactly
equal to each other or
something very close.
Schematically, the picture
is that if one thinks
about the total energy
of the universe,
it consists of a huge positive
amount in the form of matter
and radiation-- the
stuff that we see,
the stuff that we
normally identify
the energy of-- but there's
also a huge negative amount
of energy in the gravitational
field that fills the universe.
And as far as we
can tell, the sum
is at least consistent
with being 0.
In any case, what
happens during inflation
is the black bar goes up
and the red bar goes down.
And they go up and
down by equal amounts.
So certainly what happens during
inflation conserves energy,
as anything consistent with the
laws of physics that we know of
must conserve energy.
I just remembered I was planning
to turn out these blackboard
lights.
It probably makes it a
little more comfortable
to watch the screen.
OK.
So, onward.
I want to talk some about
the evidence for inflation.
So far I've described
what inflation is--
and I'm sort of done describing
what inflation is for today.
As I said, we'll be coming
back and talking about all this
during the coming semester.
Now let's move on to
discuss some of the reasons
why we think that our universe
may very likely have actually
undergone this process
called inflation
I was just telling you about.
So there are three things
I want to talk about.
The first of which is the
large scale uniformity
of the universe.
Which is related to what I
told you at the beginning,
that if you look out
in different directions
in the universe, it really looks
the same in all directions.
And the object that can
be measured with the most
precision in terms of how
things vary with angle,
is the cosmic
background radiation--
because we can measure
it from all directions,
and it's essentially
a uniform background.
And when that's been
done, what's been found
is that the radiation is uniform
to the incredible accuracy
of about one part in
100,000-- which really
is a rather spectacular
level of uniformity.
So it means the universe really
is rather incredibly uniform.
I might mention one proviso here
just to be completely accurate.
When one actually just goes
out and measures the radiation,
one finds something-- one
finds an asymmetry that's
larger than what I just said.
One finds an asymmetry
of about 1 part in 1,000,
with one direction being hotter
than the opposite direction.
But that 1 part in 1,000 effect
we interpret as our motion
through the cosmic background
radiation, which makes it
look hotter in one
direction and colder
in the opposite direction.
And the effect of our motion
has a very definite angular
pattern.
We have no other way of
knowing what our velocity is
relative to the cosmic
background radiation.
So we just measure it
from this asymmetry,
but we're restricted.
We can't let it
account for everything.
Because it has a very
different angular form,
we only get to
determine one velocity.
And once we determine that,
that determines one asymmetry
and you can subtract that out.
And then the
residual asymmetries,
the asymmetries that we cannot
account for by saying that
the Earth has a certain
velocity relative to the cosmic
background radiation, those
asymmetries are at the level
of 1 part in 100,000.
And this is 1 part in
100,000 that we attribute
to the universe and not to
the motion of the earth.
OK.
So to understand
the implications
of this incredible
degree of uniformity,
we need to say a
little bit about what
we think the history of this
cosmic background radiation
was.
And what our theories
tell us-- and we'll
be learning about
this in detail--
is that in the
early period-- Yes.
AUDIENCE: I'm sorry.
I'm curious.
When they released
WMAP and stuff,
did they already subtract
out the relativistic effect?
PROFESSOR: Well, the answer
is that they analyze things
according to angular
patterns and how
they fit different
angular patterns.
So in fact, I think they don't
even report it with WMAP,
but it would be what
they would call L
equals 1, the dipole term.
They analyze the dipole,
quadrupole, octupole, et
cetera.
So it really does not
contribute at all to anything
except that L
equals 1 term, which
is one out of 1,800
things that they measure.
So basically, I
think they don't even
bother reporting
that one number,
and therefore it's
subtracted out.
OK.
Do feel free to ask
questions, by the way.
I think it's certainly
a small enough class
that we can do that.
OK.
So what I was about to
say is that this radiation
during the early period of the
universe, when the universe was
a plasma, the radiation
was essentially
locked to the matter.
The photons were moving
at the speed of light,
but in the plasma there's
a very large cross section
for the photons to scatter
off of the free electrons
in a plasma.
Which basically means that the
photons move with the matter--
because when they're
moving on their own,
they just move a
very short distance
and then scatter, and then
move in a different direction.
So relative to the
matter, the photons
go nowhere during the
first 400,000 years
of the history of the universe.
But then at about 400,000
years the universe
cools enough-- this
is all according
to our calculations--
the universe cools
enough so that the
plasma neutralizes.
And when the plasma neutralizes,
it becomes a neutral gas
like the air in this room.
And the air in this room seems
completely transparent to us,
and it turns out
that actually does
extrapolate to the universe.
The gas that filled the universe
after it neutralized really
was transparent, and it means
that a typical photon that we
see today in the cosmic
background radiation
really has been traveling on
a straight line since about
400,000 years
after the Big Bang.
Which in turn means that when
we look at the cosmic background
radiation, we're
essentially seeing
an image of what the universe
looked like at 400,000 years
after the Big Bang.
Just as the light traveling
from my face to your eyes
gives you an image
of what I look like.
So that's what we're seeing--
a picture of the universe
at the age of 400,000
years, and it's
bland-- uniform to
1 part in 100,000.
So the question then
is, can we explain
how the universe
to be so uniform?
And it turns out that if you--
Well, I should say first of all
that if you're
willing to just assume
that the universe started out
perfectly uniform to better
than one part in
100,000, that's OK.
Nobody could stop
you from doing that.
But if you want to try to
explain this uniformity
without assuming that it was
there from the beginning, then
within the context of the
conventional Big Bang theory,
it's just not possible.
And the reason is that within
the evolution equations
of the conventional Big Bang
theory, you can calculate--
and we will calculate
later in the course--
that in order to smooth things
out in time for it to look
smooth in the cosmic
background radiation,
you have to be able to move
around matter and energy
at about 100 times
the speed of light.
Or else you just couldn't do it.
And we don't know of anything
in physics that happens faster
than the speed of light.
So within physics as we know it,
and within the conventional Big
Bang theory, there's no way to
explain this uniformity except
to just assume that maybe it was
there from the very beginning.
For reasons that we
don't know about.
On the other hand, inflation
takes care of this very nicely.
What inflation does
is it adds this spurt
of exponential expansion to
the history of the universe.
And the fact that this
exponential expansion
was so humongous
means that if you
look at our picture
of the universe
before the inflation
happened, the universe
would have been vastly smaller
than in conventional cosmology
which would not have this
exponential spurt of expansion.
So in the inflationary
model there
would've been plenty of
time for the observed
part of the universe to become
uniform before inflation
started-- when it
was incredibly tiny.
And then would become uniform
just like the air in the room
here tends to spread out and
produce a uniform distribution
of air rather than having
all the air collected
in one corner.
Once that uniformity
is established
on this tiny region,
inflation would then
take over and
stretch this region
to become large enough
to include everything
that we now see,
thereby explaining
why everything that we
see looks so uniform.
It's a very simple
explanation, and it's
only possible with
inflation and not
within the conventional
Big Bang theory.
So, the inflationary solution.
In inflationary
models the universe
begins so small that uniformity
is easily established.
Just like the air in the
lecture hall-- same analogy
I used-- spreads uniformly
to fill the lecture hall.
Then inflation
stretches the region
to become large enough
to include everything
that we now observe.
OK.
So that's the first
of my three pieces
of evidence for inflation.
The second one is something
called the flatness problem.
And the question is, why was
the early universe so flat?
And the first question
maybe is, what am I
talking about when I say
the early universe was flat?
One misconception
I sometimes find
people getting is that flat
often means two dimensional.
That's not what I mean.
It's not flat like a
two dimensional pancake.
It's three dimensional.
The flat in this context
means Euclidean--
obeying the axioms of
Euclidean geometry-- as opposed
to the non-Euclidean
options that
are offered by
general relativity.
General relativity allows three
dimensional space to be curved.
And if we only consider uniform
curvature, which is-- we
don't see any
curvature, actually,
but-- We know with
better accuracy
that the universe is uniform
than we do that it's flat.
So imagine in terms of
discussion of cosmology
three possible curvatures for
the universe, all of which
would be taken to be uniform.
Three dimensional curved spaces
are not easy to visualize,
but all three of
these are closely
analogous to two dimensional
curved spaces, which
are easy to think about.
One is the closed geometry
of the surface of a sphere.
Now the analogy is that the
three dimensional universe
would be analogous to
the two dimensional
surface of a sphere.
The analogy changes the
number of dimensions.
But important things get capped.
Like for example on the
surface of a sphere,
you can easily visualize--
and there's even
a picture to show
you-- that if you
put a triangle on the
surface of a sphere,
the sum of the three
angles at the vertices
would be more than 180 degrees.
Unlike the Euclidean case,
where it's always 180 degrees.
Question?
AUDIENCE: Yeah.
Is the 3D curving happening
in a fourth dimension?
Just like these 2D models
assume another dimension?
PROFESSOR: Good question.
The question was,
is the 3D curvature
happening in a fourth dimension
just like this 2D curvature
is happening in a
third dimension?
The answer I guess is yes.
But I should maybe clarify
the "just like" part.
The third dimension here from
a strictly mathematical point
of view allows us to visualize
the sphere in an easy way,
but the geometry of the
sphere from the point of view
of people who study differential
geometry is a perfectly well
defined two dimensional
space without any need
for the third
dimension to be there.
The third dimension is
really just a crutch for us
to visualize it.
But that same crutch does work
in going from three to four.
And in fact when we study the
three dimensional curved space
of the closed universe, we will
in fact do it exactly that way.
We'll introduce the same crutch,
imagine it in four dimensions,
and it will be very closely
analogous to the two
dimensional picture
that you're looking at.
OK.
So one of the possibilities
is a closed geometry
where the sum of the
three angles of a triangle
is always bigger
than 180 degrees.
Another possibility
is something that's
usually described
as saddle shaped,
or a space of
negative curvature.
And in that case the sum
of the three angles--
they get pinched, and
the sum of the angles
is less than 180 degrees.
And only for the flat case is
the sum of the three angles
exactly 180 degrees, which is
the case of Euclidean geometry.
The geometries on the
surfaces of these objects
is non-Euclidean,
even though if you
think of the three dimensional
geometry of the objects
embedded in three dimensional
space, that's still Euclidean.
But the restricted geometry to
the two dimensional surfaces
are non-Euclidean there and
there, but Euclidean there.
And that's exactly the way it
works in general relativity.
There are closed universes with
positive curvature and the sum
of angles being more
than 180 degrees.
And there are open universes
where the sum of three angles
is always less than 180 degrees.
And there's the
flat case-- which
is just on the
borderline of those two--
where Euclidean geometry works.
And the point is
that in our universe,
Euclidean geometry
does work very well.
That's why we all learned
it in high school.
And in fact we have
very good evidence
that the early universe
was rather extraordinarily
close to this flat case
of Euclidean geometry.
And that's what we're trying
to understand and explain.
According to general relativity
this flatness of the geometry
is determined by
the mass density.
There's a certain value
of the mass density called
the critical density-- which
depends on the expansion rate,
by the way, it's not a
universal constant of any kind.
But for a given
expansion rate one
can calculate a
critical density,
and that critical
density is the density
which makes the universe flat.
And cosmologists define a number
called omega-- capital omega--
which is just the ratio
of the actual mass
density to the
critical mass density.
So omega equals 1 says
the actual density is
the critical
density, which means
the universe would be flat.
Omega bigger than 1 would be
a closed universe, and omega
less than 1 would
be an open universe.
What's peculiar about the
evolution of this omega
quantity is that omega
equals 1 as the universe
evolves in
conventional cosmology
behaves very much like a
pencil balancing on its tip.
It's an unstable
equilibrium point.
So in other words, if omega
was exactly equal to 1
in the early universe, it would
remain exactly equal to 1.
Just like a pencil that's
perfectly balanced on its tip
would not know which way to
fall and would in principle stay
there forever.
At least with
classical mechanics.
We won't include quantum
mechanics for our pencil.
Classical pencil that we're
using for the analogy.
But if the pencil leans just
a tiny bit in any direction,
it will rapidly start to
fall over in that direction.
And similarly if omega
in the early universe
was just slightly
greater than 1,
it would rapidly rise
towards infinity.
And this is a closed universe.
Infinity really means
the universe has reached
its maximum size, and it
turns around and collapses.
And if omega was
slightly less than 1,
it would rapidly
dribble off to 0,
and the universe would
just become empty
as it rapidly expands.
So the only way for omega
to be close to 1 today--
and as far as we can
tell, omega is consistent
with 1 today-- the only
way that can happen
is if omega started out
unbelievably close to 1.
Unless it's this pencil
that's been standing there
for 14 billion years and
hasn't fallen over yet.
Numerically, for omega to be
somewhere in the allowed range
today, which is
very close to 1, it
means that omega at one
second after the Big Bang
had to be equal to 1 to the
incredible accuracy of 15
decimal places.
Which makes the value
of the mass density
of the universe at one second
after the Big Bang probably
the most accurate number
that we know in physics.
Since we really know it
to 15 decimal places.
So if it wasn't
in that range, it
wouldn't be in the
[? lab manuals ?] today.
We have this
amplification effect
of the evolution
of the universe.
So the question is,
how did this happen?
In conventional Big Bang theory,
the initial value of omega
could have been
anything, logically.
To be consistent with
what we now observe it
has to be within this
incredibly narrow range,
but there's nothing
in the theory which
causes it to be in
that narrow range.
So the question
is, why did omega
start out so
incredibly close to 1?
Like the earlier problem
about homogeneity,
if you want to just assume
that it started out-- exactly
like, it had to be-- at omega
equals 1, you could do that.
But if you want to have any
dynamical explanation for how
it got to be that
way, there's really
nothing in conventional
cosmology which does it.
But in fact, inflation does.
In the inflationary model we've
changed the evolution of omega
because we've turned gravity
into a repulsive force instead
of an attractive force, and that
changes the way omega evolves.
And it turns out that
during inflation, omega
is not driven away
from 1-- as it
is during the entire rest of
the history of the universe--
but rather during inflation
omega is driven rapidly
towards 1, exponentially
fast, even.
So with the amount
of inflation that we
talked about-- inflation by a
factor of 10 to the 28 or so--
that's enough so that the
value of omega before inflation
is not very much constrained.
Omega could have started out
before inflation not being 1,
but being 2 or 10 or
1/10 or 100 or 1/100.
The further away you
start omega from 1,
the more inflation you need
to drive it to 1 sufficiently.
But you don't need
much more inflation
to make it significantly
far away from 1
because of this fact the
inflation drives omega
to 1 exponentially.
Which really means it's a
very powerful force driving
omega to 1.
And giving us a very
simple, therefore,
explanation for why omega
in the early universe
appears to have been
extraordinarily close to 1.
So I think that's-- Oh, I
have a few more things to say.
There's actually a prediction
that comes out of this,
because this tendency of
inflation to drive omega to 1
is so strong, that you
expect that omega really
should be 1 today.
Or to within
measurable accuracy.
You could arrange
inflationary models
where it's say, 0.2--
which is what people used
to think it was-- but in order
to do that, you have to arrange
for inflation to end
at just the right time
before it makes it closer.
Because every e-fold drives it
another factor of 10 closer.
So it's very rapid effect.
So if you don't fine tune
things very carefully, most
any inflationary model will
drive omega so close to 1
that today we would see it as 1.
That did not used to
appear to be the case.
Before 1998 astronomers
were pretty sure
that omega was only 0.2 or
0.3, while inflation seemed
to have a pretty clear
prediction that omega should
be 1.
This personally I found rather
uncomfortable, because it meant
whenever I had dinner
with astronomers,
they would always sort
of snidely talk about
how inflation was
a pretty theory,
but it couldn't be right
because omega was 0.2,
and inflation was
predicting omega is 1.
And it just didn't fit.
Things changed a lot in 1998,
and now the best number we
have-- which comes from the
Planck satellite combined with
a few other
measurements, actually--
is that now the observational
number for omega is 1.0010,
plus or minus 0.0065.
So the 0.0065 is
the important thing.
This is very, very close
to 1, but the error bars
are bigger than this difference.
So it really means to about
a half a percent or maybe 1%,
we know today that
omega is 1, which
is what inflation would predict.
That it should essentially
be exactly 1 today.
The new ingredient that
made all this possible,
that drove-- changed
the measurement of omega
from 0.2 to 1 is
a new ingredient
to the energy budget of the
universe, the discovery of what
we call dark energy.
And we'll be learning
a lot about dark energy
during the course of the term.
The real discovery in 1998
was that the universe is not
slowing down under the
influence of gravity
as had been expected until that
time, but rather the universe
actually is accelerating.
And this acceleration has to
be attributed to something.
The stuff that it's attributed
to is called the dark energy.
And even though there's
considerable ignorance
of what exactly
this dark energy is,
we can still calculate
how much of it
there's got to be in order to
produce the acceleration that's
seen.
And when all that
is put together,
you get this number, which is
so much nicer for inflation
than the previous number.
Yes.
AUDIENCE: So, was the
accelerating universe
like the missing factor which
they-- gave a wrong assumption
which made them think
that omega was 0.2 or 0.3?
PROFESSOR: Yeah, that's right.
It was entirely
because they did not
know about the
acceleration at that time.
They in fact were accurately
measuring the stuff
that they were looking at.
And that does only
add up to 0.2 or 0.3.
And this new ingredient,
the dark energy,
which we only know about
through the acceleration,
is what makes the difference.
Yes.
AUDIENCE: And that data
that they were measuring
is really just sort of
the integrated stuff
in the universe that we
see through telescopes?
Very straight-forward
in that way?
PROFESSOR: That's right.
Including dark matter.
So it's not everything
that we actually see.
There's also-- not
going into it here,
but we will later in the
course-- there is also stuff
called dark matter, which is
different from dark energy.
Even though matter and energy
are supposed to be the same,
they are different
in this context.
And dark matter is
matter that we infer
exists due to its
effect on other matter.
So by looking, for example,
at how fast galaxies rotate,
you can figure out
how much matter
there must be inside
those galaxies
to allow those
orbits to be stable.
And that's significantly more
matter than we actually see.
And that unseen matter is
called the dark matter,
and that was added
into the 0.2 or 0.3.
The visible matter
is only about 0.04.
OK.
So, so much for the
flatness problem.
Next item I want talk about is
the small scale nonuniformity
of the universe.
On the largest
scale, the universe
is incredibly uniform-- one
part in 100,000-- but on smaller
scales, the universe
today is incredibly lumpy.
The earth is a big lump
in the mass density
distribution of the universe.
The earth is in fact
about 10 to the 30 times
denser than the average matter
density in the universe.
It's an unbelievably
significant lump.
And the question is, how
did these lumps form?
Where did they come from?
We are confident that
these lumps evolved
from the very
minor perturbations
that we see in the
early universe,
that we see most clearly
through the cosmic background
radiation.
The early universe we believe
was uniform in its mass density
to about one part in 100,000.
But at the level of
one part in 100,000,
we actually see in the
cosmic background radiation
that there are nonuniformities.
And things like the
Earth form because
these small nonuniformities
in the mass density
are gravitationally unstable.
In regions where there's
a slight excess of matter,
that excess of matter
produces a gravitational field
pulling more matter
into those regions,
producing a still stronger
gravitational field pulling
in more matter.
And the system is unstable,
and it forms complicated lumps
which are galaxies,
stars, planets, et cetera.
And that's a complicated story.
But it all starts from these
very faint nonuniformities that
existed, we believe,
shortly after the Big Bang.
And we see these nonuniformities
in the cosmic background
radiation, and
measuring them tells us
a lot about the
conditions of the universe
then, and allows us
to build theories
of how the universe
got to be that way.
And that's what these satellites
like COBE, WMAP, and Planck
are all about-- measuring
these nonuniformities
to rather
extraordinary accuracy.
Inflation has an
answer to the riddle
of where the
nonuniformities came from.
In the conventional
Big Bang theory,
there was really
just no explanation.
People just assumed they were
there and put them in by hand,
but there was no theory of
what might have created them.
In the context of
inflationary models
where all the matter really is
being created by the inflation,
the nonuniformities are also
controlled by that inflation,
and where nonuniformities
come from is quantum effects.
It's a little hard to believe
that quantum effects could
be important for the large
scale structure of the universe.
The Andromeda
galaxy doesn't look
like it's something
that should be
thought of as a
quantum fluctuation.
But when one pursues this
theory quantitatively,
it actually does work very well.
The theory is that
the ripples that we
see in the cosmic
background radiation
really were purely the
consequence of quantum theory--
basically the uncertainty
principle of quantum theory,
which says that it's just
impossible to have something
that's completely uniform.
It's not consistent with
the uncertainty principle.
And when one puts in the basic
ideas of quantum mechanics,
we can actually calculate
properties of these ripples.
It turns out that we
would need to know
more about the physics
of very high energy--
the physics that was
relevant during the period
of inflation-- to
be able to predict
the actual amplitude
of these ripples.
So we cannot predict
the amplitude.
In principle, inflation
would allow you
to if you knew enough about the
underlying particle physics,
but we don't know that much.
So in practice we cannot
predict the amplitude.
But inflationary models
make a very clear prediction
for the spectrum of
these fluctuations.
And by that I mean how
the intensity varies
with wavelength.
So the spectrum really
means the same thing
as it would mean for
sound, except you
should think about wavelength
rather than frequency
because these waves
don't really oscillate.
But they do have wavelengths
just like sound waves have
wavelengths, and if you
talk about the intensity
versus wavelengths,
this idea of a spectrum
is really the same
as what you'll
be talking about with sound.
And you can measure it.
This is not quite the
latest measurements,
but it's the latest measurements
that I have graphed.
The red line is the
theoretical prediction.
The black dots are
the measurements.
This goes through the
seven year WMAP data.
We have a little
Eureka guy to tell you
how happy I am about this curve.
And I also have graphs of what
other ideas would predict.
For a while, for example, people
took very seriously the idea
that the randomness that
we see in the universe--
these fluctuations--
may have been caused
by the random
formation of things
called cosmic strings
that would form
in phase transitions
in the early universe.
That was certainly a
viable idea in its day,
but once this
curve got measured,
the cosmic strings were
predicting something
that looked like that, which is
nothing at all like that curve.
And they have since
been therefore excluded
as being the source of density
fluctuations in the universe.
And various other
models are shown here.
I don't think I'll take the time
to go into, because there are
other things I
want to talk about.
But anyway, marvelous success.
This is actually
the latest data.
This is the Planck data that
was released last March.
I don't have it plotted
on the same scale,
but again you see
a theoretical curve
based on inflation
and dots that show
the data with little
tiny error bars.
But absolutely gorgeous fit.
Yes.
AUDIENCE: What happened to
your theory of inflation
after they discovered
dark energy?
Did it change significantly?
PROFESSOR: Did
the theory change?
AUDIENCE: Or like,
in the last graph
there was a different curve.
PROFESSOR: Well it's plotted
on a different scale,
but this actually is pretty much
the same curve as that curve.
Although you can't tell.
AUDIENCE: Sorry.
PROFESSOR: Oh.
Oh, inflation without
dark energy, for example.
I think it's not so much
that the theory of inflation
changed between
these two curves,
but the curve you
actually see today
is the result of what things
looked like immediately
after inflation combined with
the evolution that took place
since then.
And it's really
the evolution that
took place since then that
makes a big difference
between this inflationary curve
and the other inflationary
curve.
So inflation did not have
to change very much at all.
It really did not.
But of course it
looks a lot better
after dark energy was discovered
because the mass density came
out right, and gradually we
also got more and more data
about these fluctuations
which just fit beautifully
with what inflation predicts.
OK.
I want to now launch into
the idea of the multiverse.
And I guess I'll try to go
through this quickly so that we
can finish.
We're not going try to
understand all the details
anyway, so I'll talk
about fewer of them
for the remaining 10
minutes of the class.
But I'd like to say a little
bit about how inflation
leads to the idea
of a multiverse.
Of course we'll come back to it
at the very end of the class,
and it's certainly an exciting,
I think, aspect of inflation.
The repulsive gravity material
that drives the inflation
is metastable, as we said.
So it decays.
And that means that if
you sit in one place
and ask where
inflation is happening,
and ask what's the probability
that it's still happening
a little bit later,
that probability
decreases exponentially--
drops by a factor of two
every doubling, every half life.
But at the same time, the volume
of any region that's inflating
is also growing exponentially,
growing due to the inflation.
And in fact in any
reasonable inflationary model
the growth rate is vastly
faster than the decay rate.
So if you look at
the volume that's
inflating, if you
wait for a half life,
indeed half of that
volume will no longer
be inflating-- by the
definition of a half life.
But the half that remains
will be vastly larger
than what you started with.
That's the catch.
And that's a very
peculiar situation
because it doesn't
seem to show any end.
The volume that's inflating
just gets bigger and bigger
even while it's decaying,
because the expansion is faster
than the decay.
And that's what leads to this
phenomena of eternal inflation.
The volume that is inflating
increases with time,
even though the inflating
material is decaying.
And that leads to what we
call eternal inflation.
The word "eternal" is
being used slightly loosely
because eternal
really means forever.
This is forever into the
future, as far as we can tell,
but it's not forever
into the past.
Inflation would still start
at some finite time here,
but then once it starts,
it goes on forever.
And whenever a piece of
this inflating region
undergoes a transition
and becomes normal,
that locally looks
like a Big Bang.
And our Big Bang would be
one of these local events,
and the universe formed by
any one of these local events
where the inflating
region decays
would be called a
pocket universe.
Pocket just to suggest
that there are many of them
in the overall scale
of this multiverse.
They are in some sense
small, even though they'd
be as big as the
universe that we live in.
And our universe would be one
of these pocket universes.
So instead of one
universe, inflation
produces an infinite
number, which
is what we call multiverse.
I might just say the
word multiverse is also
used in other contexts
and another theories,
but inflation, I think, is
probably the most plausible way
of getting a
multiverse, and it's
what most cosmologists
are talking
about when they talk
about a multiverse.
OK.
Now how does dark
energy fit in here?
It plays a very important
role in our understanding.
To review, in 1998
several groups--
two groups of astronomers
discovered independently
that the universe
is now accelerating,
and our understanding
is that the universe has
been accelerating for about
the last five billion years
out of the 14 billion year
history of the universe.
There was a period where
it was decelerating
until five billion years ago.
An implication of this is
that inflation actually
is happening today.
This acceleration of
the universe that we see
is very much like inflation,
and we really interpret it
according to similar
kind of physics.
We think it has to be
caused by some kind
of a negative pressure,
just as inflation
was caused by a
negative pressure.
And this material that
apparently fills space and has
negative pressure is
what we call dark energy.
And dark energy is
really just by definition
the stuff, whatever
it is, that's
causing this acceleration.
If we ask, what is the
dark energy, really?
I think everybody agrees there's
a definite answer to that,
which is something
like, who knows?
But there's also a most
plausible candidate,
even though we don't know.
The most plausible candidate--
and other candidates
are not that different,
really, but we'll
talk about the most plausible
candidate-- which is simply
that dark energy
is vacuum energy.
The energy of nothingness.
Now it may be surprising that
nothingness can have energy.
But I'll talk about that, and
it's really not so surprising.
I'll come back to that question.
But if dark energy is really
just the energy of the vacuum,
that's completely
consistent with everything
we know about, what we can
measure, the expansion pattern
of the universe.
Yes.
AUDIENCE: Why is it that only
in the last five billion years
has the universe
started accelerating?
PROFESSOR: To
start accelerating.
Right.
Right.
OK.
I'm now in a
position to say that.
I wasn't quite when I
made the first statement,
but now that I've said there's
probably vacuum energy,
I can give you an answer.
Which is that vacuum
energy, because it is just
the energy of the vacuum,
does not change with time.
And that's the same as what
I told you about the energy
density during inflation.
It's just a constant.
At the same time,
ordinary matter
thins out as the universe
expands, throwing off
in density like one over
the cube of the volume.
So what happened was
that the universe
was dominated by ordinary
matter until about five
billion years ago, which
produced attractive gravity
and caused the universe to slow.
But then about five
billion years ago
the universe thinned out enough
so that the ordinary matter
no longer dominated over
the vacuum energy, and then
the vacuum energy started
causing repulsion.
Vacuum energy was there all
along causing repulsion,
but it was overwhelmed
by the attractive gravity
of the ordinary matter until
about five billion years ago.
Does that make sense?
AUDIENCE: Yes.
PROFESSOR: OK.
Good.
Any other questions?
OK.
So.
The first thing I want
to talk about here
is why can nothing
weigh something?
Why can nothing have energy?
And the answer is
that actually this
is something the physicists
are pretty clear on these days.
The quantum vacuum, unlike
the classical vacuum,
is a very complicated state.
It's not really empty at all.
It really is a complicated
jumble of vacuum fluctuations.
We think there's even a field
called the Higgs field, which
you've probably
heard of, which has
a nonzero value in
the vacuum on average.
Things like the photon field,
the electromagnetic field,
is constantly oscillating
in the vacuum because
of the uncertainty
principle, basically,
resulting in energy density
in those fluctuations.
So there's no reason
for the vacuum energy
to be zero, as far
as we can tell.
But that doesn't mean that
we understand its value.
The real problem from the point
of view of fundamental physics
today is not understanding
why the vacuum might
have a nonzero energy density.
The problem is understanding
basically why it's so small.
And why is smallness a problem?
If you look at quantum field
theory-- which we're not
going to learn in any detail--
but quantum field theory
says that, for example,
the electromagnetic field
is constantly fluctuating.
Guaranteed so by the
uncertainty principle.
And these fluctuations
can have all wavelengths.
And every wavelength contributes
to the energy density
of the vacuum fluctuations.
And there is no
shortest wavelength.
There's a longest
wavelength in any size box,
but there's no
shortest wavelength.
So in fact, when you try
to calculate the energy
density of the vacuum in
the quantum field theory,
it diverges on the
short wavelength side.
It becomes literally infinite
as far as the formal calculation
is concerned because all
wavelengths contribute,
and there is no
shortest wavelength.
So what does this mean
about the real physics?
We think it's not necessarily a
problem with our understanding
of quantum field theory.
It really is, we think,
just a limitation
of the range of validity
of those assumptions.
They certainly-- quantum theory
works extraordinarily well
when it's tested in
laboratory circumstances.
So we think that at
very short wavelengths,
something must happen to
cut off this infinity.
And a good candidate for what
happens at short wavelengths
to cut off the
infinity is the effects
of quantum gravity, which
we don't understand.
So one way of estimating
the true energy density
as predicted by
quantum field theory
is to cut things off at the
Planck scale, the energy scale,
length scale, associated
with quantum gravity-- which
is about 10 to the
minus 33 centimeters.
And if you do that, you
can calculate the number
for the energy density of
the electromagnetic field
of the vacuum and
get a finite number.
But it's too large.
And too large not by a
little bit, but by a lot.
It's too large by 120
orders of magnitude.
So we are way off in terms of
understanding why the vacuum
energy is what it is since our
naive estimates say it should
be maybe 120 orders
of magnitude larger.
Now I should add that there
is still a way out here.
The energy that
we calculate here
is one contribution to
the total vacuum energy.
There are negative
contributions as well.
If you calculate the
fluctuations of the electron
field, that turns out to be
negative in its contribution
to the energy.
And it's always possible
that these numbers cancel--
or cancel almost exactly-- but
we don't know why they should.
So basically there's a big
question mark theoretically
on what we would predict for the
energy density of the vacuum.
Let's see.
What should I do here?
I am not going to be able
to finish this lecture.
I think it's worth
finishing, however.
So I think what I'll do is I'll
maybe go through this slide
and then we'll just stop, and
we'll pick up again next time.
There are just a few
more slides to show.
But I think it's an interesting
story worth finishing.
But to come to a good
stopping place here--
we still have a minute
and a half, I think.
I want to say a little bit about
the landscape of string theory,
which is going to be a possible
explanation-- only possible,
it's very speculative here-- but
one possible explanation which
combines inflation, the eternal
inflation, and string theory
produces a possible explanation
for this very small vacuum
energy that we observe.
It's based on the idea
that string theory does not
have the unique vacuum.
For many years string
theorists sought
to find the vacuum of string
theory with no success.
They just couldn't
figure out what
the vacuum of string
theory would look like.
And then a little more than 10
years ago many string theorists
began to converge
around the idea
that maybe they could not
find a vacuum because there
is no unique vacuum
to string theory.
Instead, what they now
claim is that there's
a colossal number-- they
bandy around numbers like 10
to the 500th power-- a colossal
number of metastable states,
which are long lived,
any one of which
could look like a vacuum
for a long period of time,
even though ultimately it
might decay or tunnel into one
of the other metastable states.
So this is called the
landscape of string theory.
This huge set of
vacuum like states,
any one of which could be
the vacuum that fills a given
pocket universe, for example.
When one combines this with
the idea of eternal inflation,
then one reaches the conclusion
that eternal inflation
would very likely
populate all of these 10
to the 500 or more vacua.
That is, different
pocket universes
would have different kinds
of vacuum inside them, which
would be determined randomly as
the pocket universes nucleate,
as they break off from
this inflating backbone.
And then we would
have a multiverse
which would consist
of many, many-- 10
to the 500 or more--
different kinds of vacua
in different pocket universes.
Under this assumption,
ultimately string theory
would be the assumed
laws of physics
that would govern everything.
But if you were living in one
of these pocket universes,
you actually see apparent laws
of physics that would look very
different from other
pocket universe's.
The point is that the
physics that we actually
see and measure is low energy
physics compared to the energy
scales of the string theory.
So what we are seeing are
just small fluctuations
in the ultimate scheme of
things about the vacuum
that we live in.
So the very particle
spectrum that we see,
the fact that we see
electrons and quarks, quarks
that combine to form
protons and neutrons--
could be peculiar to
our particular pocket.
And in other pockets there could
be completely different kinds
of particles, which
are just oscillations
about different kinds of vacuum.
So even though the
laws of physics
would in principle be
the same everywhere--
the laws of string
theory-- in practice the
observed laws of
physics would be
very different from
one pocket to another.
And in particular
since there are
different vacua in
the different pockets,
the vacuum energy
density would be
different in different pockets.
And that variability of
the vacuum energy density
provides a possible answer to
why we see such a small vacuum
energy.
And we'll talk more about
that next time on Tuesday.
See you then.
