[MUSIC PLAYING]
MODERATOR: I think the
statute of limitations
has passed on telling
stories out of school.
So I'm going to do this one.
It's 12 years ago or
so since when he came.
One day, he was at Cornell, had
been a student of Francis Low.
And one day, he called me
up and he said he really
wanted to come back to MIT.
We weren't looking for
anyone at the time.
Did he want to come back to MIT?
I hope you'll forgive me, Alan.
And he knew that he
was too old to come in
as an assistant professor.
And he'd be willing to take the
risk of coming back at a level
where the risk of
tenure comes sooner.
I brought it up with
the theory group,
with the high energy group.
And we knew that it was a
difficult kind of situation.
But we did it anyway.
We took the risk.
Well, here's our risk.
[LAUGHTER]
GUTH: Thanks.
He collected my first
line right away.
Those of you who know
me know that I usually
have in my title transparency, a
cartoon of a well-known cartoon
character.
But the organizers
of this conference
took the precaution of
having all the speakers sign
an affidavit saying that they
actually had obtained the right
to use all of the visuals that
they use during their talks.
So sorry, folks.
No cartoon.
We'll have to do without that.
[LAUGH]
I'm going to be talking
about some of the impact
that modern particle physics
has had on cosmology.
As you probably known, a small
drove of particle theorists
began to dabble in cosmology
back in the late 1970s.
And I became part of that drove.
A lot of our colleagues felt
we were motivated mainly
by jealousy of Carl Sagan.
But I've always maintained
that there was also
a significant motivation,
which stems from developments
in particle physics itself.
And what I have in
mind, of course,
is the advent of grand
unified theories.
These theories were first
invented back in 1974.
But it wasn't really
until the late 1970s
that they really began to become
objects of widespread interest
in the particle
theory community.
What makes these theories
important for cosmology
is that they make their
most important predictions
at an energy scale of about 10
to the 14 or 10 to the 15 GeV.
By the standards of our
local power company,
that's not much energy.
It's about what it takes
to light a 100-watt light
bulb for a minute.
But, as you might
imagine, having
that much energy on a
single elementary particle
is, of course, extraordinary.
One could imagine trying to
build an accelerator that
would reach those energies.
One could take, for example,
the Stanford linear accelerator
and imagine scaling it up.
The output energy is essentially
directly proportional
to the length.
So it's a back-of-the-envelope
calculation to figure out how
long SLAC would have to be in
order to reach an energy of 10
to the 14 GeV.
The answer, in case you've
never done this calculation,
turns out to be almost exactly
1 in the right units, the units,
of course, being light years.
So, needless to say, the
Department of Energy and NASA
have both been very reluctant
to entertain proposals
to build such an accelerator.
And what that
means is that if we
want to be able to see the
most dramatic consequences
of these grand unified
theories, we're
really forced to turn to the
only laboratory to which we
have any access at
all, which has ever
reached these energies.
And that appears to be
the universe itself,
in its very infancy.
And that basically is the
reason why so many particle
theorists have become interested
in the early universe.
Can I have the
next transparency?
What I want to do
in today's talk,
since I now have a very
interesting experimental result
that came out just a few
weeks ago, the COBE results,
I'd like to basically
spend the beginning
part of the talk building
up to a discussion of COBE.
And then I will try to
discuss the implications
of the COBE measurements.
So I need to begin by discussing
the standard hot Big Bang
theory.
And I know that many of you are
nuclear physicists and particle
physicists, and have
not considered much
about the details of cosmology.
So I have here a
complete summary
of the important elements
of the standard Big Bang
theory in three statements.
The first statement
is the assumption
that the early universe was a
uniformly expanding, extremely
hot gas, which was in
thermal equilibrium,
or at least approximately in
thermal equilibrium, at all
times during the expansion.
So the expansion is just
the adiabatic expansion
of a thermal equilibrium gas,
something which, of course,
we've all learned how to
treat in our statnet courses.
In the early universe, the
mass density, we believe,
was completely dominated
by black-body radiation,
not by the matter
that now dominates
the mass of the universe.
And that makes it, of course,
a very simple system to treat.
All of the properties
of this gas
are completely determined
once you know the temperature.
And you can calculate how
fast the temperature changes
because you can calculate
the dynamics of the expansion
and cooling.
The third assumption
is what makes
that calculation possible.
The assumption that the
only significant force
in the early
universe is the force
of gravity, which is
gradually slowing down
the expansion due to the
gravitational attraction
of everything for
everything else.
This, of course, in
cosmology is generally
treated using
general relativity.
But, in fact, you can use
Newton's laws of mechanics.
And they work almost as well.
And, in many cases,
give identical answers.
Next transparency.
Okay.
So much for standard cosmology.
Now, I'll move
right along and get
into the topic of inflation.
Because what I'd like
to do is to explain some
of the consequences of
inflation and to what extent
they've been tested by
the COBE measurements.
So I want to explain to you
the mechanism behind inflation
because I think it all seems
very mysterious, if one doesn't
have some notion of
how inflation works.
So I'd like to go through
this reasonably quickly.
Inflation is driven
by a scalar field.
And the first thing
I want to point out
is that scalar fields are very
commonplace to all particle
theorists.
They're essential ingredients
of the Glasgow-Weinberg-Salam
model of electroweak
interactions.
They're also an
essential ingredient
of grand unified theories.
The modern superstring theories
do not have fundamental scalar
particles.
In fact, they do not have
fundamental particles at all.
The fundamental ingredients
in those theories are strings.
But nonetheless, even
in these theories,
at energies well below
the Planck scale of 10
to the 19 GeV, the
theories are believed
to be well approximated
by our good
old-fashioned quantum field
theories, in which one
has real particles.
And in fact, the
superstring theories always
give rise to a
reasonably large number
of what appear to be
fundamental scalars
in this low-energy
approximation.
Next transparency.
It is typical of a Higgs field
that the potential energy
function has a minimum at
some value other than 0.
Now, the field that
drives inflation
is actually almost certainly
not the Higgs field
of either the
Weinberg-Salam model
or the Higgs field of
the grand unified theory.
But, nonetheless, it is
patterned on that model.
So I will assume that the
minimum energy of the scalar
field is at some non-zero
value, here called phi
sub t, t for true vacuum.
Remember, the definition of
the vacuum in this context
is simply the state of lowest
possible energy density.
So that is, by definition
then, the vacuum.
However, the potential
energy function
could also somewhere else
have a plateau or perhaps
another local minimum.
That can be a metastable state.
That is, if the plateau
is gentle enough,
it can take a very long time
before a scalar field perched
on top of that plateau can find
its way to roll down the hill,
especially by the time
scales of the early universe.
It is that metastable state
which is called a false vacuum.
That is, a false
vacuum is simply
a state in some region of space
where the scalar field has
the value that's
here called phi sub
f, the value at the
top of the plateau.
The energy is then dominated
by this scalar field.
And the energy
density I will call
rho sub f, f for false vacuum.
Next transparency.
I tried to explain here
where the word "false vacuum"
comes from.
It may be more or
less obvious by now.
A vacuum is being used in
the sense of state of lowest
possible energy density.
This clearly is not the state of
lowest possible energy density.
The scalar field could roll down
the hill and find the bottom.
But the assumption is that
that takes a long time.
So temporarily, this acts
as if the energy is already
as low as it can get.
So what we have is
a temporary vacuum.
And the word "false"
is being used
to denote that notion
of temporariness.
Now, just knowing the fact
that the energy density of this
false vacuum cannot be lowered,
at least on an appropriate time
scale, that's all one needs
to actually derive what is its
crucial property for cosmology,
which is its pressure.
We can derive is pressure by
doing a thought experiment.
Don't try to actually do
this experiment, by the way.
It's very expensive, not
to mention difficult.
But let's imagine that
we have a piston chamber
that we filled with
a false vacuum,
with this non-zero energy
density and the pressure which
we're trying to. calculate.
Outside, we just
have ordinary vacuum.
So the energy density is
0 and the pressure is 0.
What I want to imagine is
that somebody pulls out
on the plunger, enlarging the
volume of the chamber inside
by an amount dV.
Now, since the energy density
is fixed because the scalar
field just has no lower
energy state to go to,
that it can reach in the
appropriate amount of time,
the energy density
inside this chamber
will remain constant,
which is obviously
something that's very different
from any ordinary material
that we are used to.
If there was a gas
inside that, nitrogen,
it would just thin out as
you increase the volume.
But a false vacuum
cannot do that.
And that's what
makes it so different
from any other material.
So the energy density
remains constant.
The energy inside,
therefore, goes up
by the energy density
times the change in volume.
By conservation of energy,
that must be equal to the work
that the person
pulling on the plunger
has done in pulling it
out by that distance.
And that work is just minus pdV.
And that implies
immediately that p has
to be equal to minus rho sub f.
In other words,
the vacuum creates
a suction, a negative
pressure, inside this piston.
So that to pull it out,
you have to do work.
And the work you
do is just enough
so that as you pull it out,
the energy density inside
remains constant.
So what we have is a
colossal negative pressure.
Next transparency.
Now, what is the
cosmological effect
of such a negative pressure?
Well, one could put this
into Einstein's equations
to find out what they do
to a cosmological model.
And what's found is
that they act exactly
like Einstein's famous
cosmological constant, but only
temporarily, of course.
That is, it only acts
like this as long
as the false vacuum survives.
And it is only metastable,
not absolutely stable.
The effect is to slow
the cosmic expansion.
Well, excuse me.
In general, the
effect of gravity
is to slow the cosmic expansion.
And I've written
here the key equation
that describes how gravity slows
the expansion of the universe.
The expansion of the
universe is described
in terms of a scale factor, R.
R simply sets the size scale
for the entire universe, in the
sense that whenever R doubles,
it means that the entire
universe being described
has doubled in size,
all distances within it.
So it says that the
acceleration of R, R double dot,
is negative and
proportional to G,
Newton's constant, times the
mass density plus 3 times
the pressure.
The first term is
purely Newtonian.
It's exactly what you would
get from Newtonian mechanics.
The second term is
what is normally
a relativistic correction.
In this case, however,
it is by no means
a relativistic correction.
Our pressure is
negative and equal
in magnitude to
the energy density.
So the second term dominates
and actually changes
the overall sign of the
entire right-hand side
of the equation, thereby
completely reversing
the effect of gravity.
The false vacuum actually
creates a very large
gravitational repulsion.
And the expansion
of the universe
is accelerated, if the universe
is ever in a false vacuum
state, rather than having
the expansion of the universe
being slowed down,
as it normally is,
by gravitational effects.
Next transparency.
So the key behind the
inflationary model
is the assumption
that the universe went
through a short
period, during which
the matter in the
universe was dominated
by this very peculiar
state that is predicted
by many, many of our
particle theories,
the state called a false vacuum.
To take you through the
scenario of the new inflationary
universe-- the word "New" here,
by the way, as most of you
probably know, is there because
the original inflationary
universe that I proposed
in 1981 did not quite work.
There was a flaw having to do
with the way in which inflation
ended.
It did not end smoothly enough.
The first working
version of inflation
was that the so-called new
inflationary model, posed
independently by Andrei Linde
and Albrecht and Steinhardt
in 1982.
And what I'll basically
be describing here today
is the new
inflationary universe,
although now there are
several other working versions
of inflation, in addition.
The key idea is the belief that
a small patch of the universe--
it doesn't have to be
the whole universe.
And it doesn't have
to be very large.
10 to the minus 24
centimeters across will do.
A small patch of
the early universe
somehow settled into
a false vacuum state.
There are a number of ideas
about how this can happen.
In fact, in many
of these theories,
this is the thermal equilibrium
state at high temperatures.
So if the universe
simply cools quickly,
it would supercool into
one of these false vacua.
In any case, once you
assume that this happens
for one reason or
another, everything else
is really pretty well dictated.
One doesn't have much in
the way of other choices
beyond the assumptions
that one has
to make to get into
the false vacuum
and start inflation
in the first place.
Then this patch of space
will start to expand.
It expands exponentially.
And what you need is
for the false vacuum
to be sufficiently stable so
that that exponential expansion
encompasses at least
25 orders of magnitude.
It can, by the way, be
much more than that.
No fine-tuning is
necessary to cut that off.
No matter how large that
is, it's okay as far
as the predictions of inflation.
But one does need a
number at least this large
in order for inflation
to solve the problems
that it was intended to solve.
During this time,
the particle density
then is essentially driven to
0 by the enormous exponential
expansion.
If there were any bumps or lumps
in the metric of space itself,
they are also smoothed out
by the enormous expansion.
So just like the surface of the
Earth always looks flat to us,
even though we know
it's really round,
any fold or bend in
the metric of space
gets stretched to
the point where
it becomes completely invisible
to any local observation.
There'll be a correlation
length in this early universe,
a distance over which
temperatures, and particle
velocities, and values
of fields are correlated.
That's initially very
small, but will be stretched
by this enormous expansion.
And you need to assume
that it's stretched
to the length of
about 10 centimeters
by the time inflation is over.
This is the size that what we
now call the visible universe
would have had at
the end of inflation.
And that's where this
number comes from.
Then, the normal
evolution of the universe
at the end of inflation
takes this size scale
and stretches it out to be the
presently observed universe.
Eventually, the
false vacuum decays.
It's only metastable,
not absolutely stable.
When it does, it releases
this colossal energy density.
That produces particles, which
scatter off of each other,
producing more particles.
And very quickly, the system
reaches thermal equilibrium.
And what you have is
a hot soup of gas,
uniformly spread through
space, expanding uniformly,
which is exactly
what has always been
the assumed starting point
of the standard cosmological
model.
So the effect of
inflation is simply
to establish the
initial conditions
for standard cosmology, which
then takes over at this time.
Next transparency.
We need to make the baryons
that we see in the universe.
Any baryons that might have
been present before inflation
would get diluted away by
the enormous expansion,
just like anything else.
So it is essential, in
an inflationary model,
to have an underlying particle
physics, in which baryon number
is not conserved,
so that baryons can
be produced after inflation.
Fortunately, most
modern particle theories
have this property.
So it does not seem to
be any kind of a barrier.
I want to point out that
if inflation is right,
it means that essentially
all of the matter
and energy in the
observed universe
was actually produced during
this exponential expansion
and then subsequent decay--
I think I lost--
that still works--
then the subsequent decay
of the false vacuum.
You might wonder what happens
to conservation of energy,
and I thought you might.
So I put it on the
transparency here.
What happens to
conservation of energy
is that it turns out that the
gravitational field itself
gives a negative contribution
to the total energy.
And what happens
during inflation
is that more and
more positive energy
appears in the form of an
enlarged regional false vacuum
as the exponential
expansion takes place.
But at the same time,
a compensating amount
of negative energy appears
in the enlarged volume
of the gravitational field.
And the net result is
that energy is conserved.
It remains constant.
And it remains at all times,
in fact, incredibly small.
And it could even be exactly 0.
It is quite consistent
with everything
we know that the gravitational
energy of the universe
might precisely
cancel the energy
that we see in the form of
stars, and galaxies, and so on.
Next transparency.
You might wonder why
people would perhaps
believe that inflation
may have taken place.
Well, inflation does
answer questions
about a number of the
fundamental properties
that the universe has, which
otherwise go unexplained.
Many of these properties
are properties
that are so obvious that people
have grown to accept them
without ever feeling that
they needed to be explained.
But the nice thing
about inflation
is that it does explain it.
And once one has an explanation,
one becomes fond of it
and one tends to look down on
other possibilities in which
the explanation gets lost.
So let me just
summarize what some
of these properties
of the universe
are that inflation can explain.
The first one is simply the
bigness of the universe.
The universe, as you know, is
really very, very, very big.
The number of
particles, for example,
is at least as big as 10 to
the 90, which is probably
about the largest number
you're likely to come across
in physics.
The question is simply where
did they all come from?
They're in the standard
cosmological model.
Most people probably
don't realize this.
But you start out
assuming that all 10
to the 90 of these
particles are already there.
The model contains
no mechanism whatever
for the creation
of the particles
or of the matter in any form.
In the inflationary model,
however, you don't need that.
All you need is the small patch
of false vacuum, which people
now hope might
materialize as a quantum
fluctuation or something.
That's, of course,
still very speculative.
But in any case, you don't
need anything like the 10
to the 90 particles
that you need in order
to start off a standard
cosmological model
of the universe.
The second feature is
the Hubble expansion,
which, of course, is very well
known, discovered back in 1929.
Inflation leads to it naturally.
The exponential
expansion is driven
by the repulsion of the
gravitational effects
of the false vacuum and sets
the universe out in this motion.
What's going on here
is the basic fact
that, again, is not very well
publicized, that the Big Bang
theory does not in any way
contain a theory of the bang.
The Big Bang theory,
as it was developed
in the early part
of this century,
is really the theory of
the aftermath of a bang,
without any explanation as
to what it was that banged.
Inflation is an answer
to that question.
It would be this
exponential expansion
of the false vacuum,
that really would
be the bang of the Big Bang.
Third, the question of
homogeneity and isotropy.
The universe is known to
be incredibly uniform.
The cosmic background
radiation, which
is what I'll be
coming to shortly,
is known to be uniform, same
temperature in all directions,
to accuracies of one part in
10 to the 5, extreme accuracy.
Now, in the standard
cosmological model,
that radiation, if you look
in different directions,
is coming from matter,
which at the time
the radiation was emitted,
those different pieces of matter
had not even had time to
communicate with each other
at the speed of light.
In fact, they missed by
about a factor of a hundred.
So in the standard
cosmological model,
there is no
explanation whatever as
to why the temperature
should look
the same in all directions.
You can make it work in the
context of the standard model.
You do that by simply assuming
that the universe started out
with a completely uniform
temperature throughout.
But what one does not
have in the standard model
is any explanation whatever as
to how or why the universe was
so uniform.
In inflation, that
happens naturally
because one starts with
an incredibly small region
of space, which has had
plenty of time to come
to a uniform
temperature, the same way
a glass of water
sitting on the table
comes to a uniform temperature.
And then inflation takes over,
and takes this incredibly small
region and magnifies it so
that it becomes large enough
to encompass the entire
observed universe.
Next, the notion of what's
called flatness in cosmology.
And that is the closeness of the
actual density of the universe,
to what is called the
critical density, which
is that density which is just
barely sufficient to eventually
halt the expansion
of the universe.
Today, we don't know
very well how close
we are to the critical density.
But even with the big
uncertainties in the value
today, when you extrapolate
it backwards and ask what must
it have come from,
what you find,
if you extrapolate back
to, say, one second, which
is a very reasonable time
in classical cosmology,
it's really the beginning of
the nucleosynthesis processes,
at that time what you compute is
that the density must have been
equal to the critical density
to accuracies of the order of 15
decimal places.
In standard
cosmology, one simply
has to put that in
as an assumption
about the initial conditions,
without any explanation.
In the inflationary
model, on the other hand,
it turns out that this period
of exponential expansion
actually drives the universe
to a critical density
and does it, in fact, to a
rather extraordinary accuracy,
so that one has a clear
prediction that even
today the mass density
of the universe
should be at the critical
density if inflation is right.
Finally, there is
magnetic monopoles.
If grand unified
theories are right
and standard
cosmology were right,
it would mean that
we would just be
swimming in magnetic monopoles.
Well, in fact, that we
haven't detected or seen any.
And inflation gets rid of them
by simply inflating them away,
diluting them to a
negligible density.
Now, I'm ready to move on to
the second part of my talk.
I want to discuss the
cosmic background radiation
and what we have learned about
it in particular from the COBE
satellite.
First, I have here simply
a side of the spectrum
of the cosmic
background radiation,
as it was measured by COBE.
This is a far better
measurement than anything
that had preceded it.
I had toyed with the idea of
showing you some of the earlier
graphs just to
assure that you'd be
adequately impressed by the
graph that you're seeing now.
I decided that maybe it wasn't
worth the time to do that.
But as you can see, this is an
absolutely marvelous agreement
between the data points,
shown as these little boxes,
and the black curve, which
is a black-body spectrum.
Let me remind you that this
is only a one-parameter fit.
The only thing that's
fit is the temperature.
Once you know the
temperature, you
know not only where
the peak should be,
but exactly how high
the peak should be.
And both agree
perfectly with the data,
the same with the entire
shape of the curve.
So we have extremely
good evidence
now that the radiation
that we're seeing
is remarkably thermal.
And that's exactly
what would be expected
from primordial radiation
that is left over
from the heat of the Big Bang,
which is how this radiation is
being interpreted.
Next transparency.
Now, I want to just
try to describe here
exactly where this radiation
is really coming from.
So what I've drawn is
a spacetime diagram
of the universe.
I'm showing only two dimensions
of space, illustrated here
as the x- and y-axes, and
one direction of time, which
is all there is, going upward.
The present time is
supposed to be this dot.
And we can imagine
that we are sitting
at the position and time of
that dot, looking outward.
Now when we look
outward, what we see
is light that has been
traveling from the past.
So our past light cone,
which is basically
the light we're looking at,
goes downward in all directions.
And the further out we
look, as everybody knows,
the further into the
past we are looking.
Now, let me describe
what's supposed
to be going on at bottom
part of this diagram, which
represents the beginning of
the time of our universe.
The Big Bang is supposed
to be at time 0 here.
This gray sheet, it's
not that easy to see,
it's supposed to be
a little bit above.
It's not at time 0.
It's a little bit later.
It's supposed to be
actually at 300,000 years,
is where the gray sheet
is supposed to be.
Now, what happened
at 300,000 years?
The key thing is that
according to cosmology,
the early universe
was incredibly hot.
Actually, arbitrarily
hot, if you follow it
backwards The theoretical
t was 0 in the model.
And that means that the
matter in the early universe
would certainly not have been
in the form of neutral atoms.
It was a plasma.
And until about 300,000
years after the Big Bang,
the mass in the
universe consisted
of a plasma of
protons and electrons,
and also neutrinos and
photons, and so on.
In this hot plasma,
photons are constantly
being rescattered by the charged
particles moving through space.
And this plasma is very dense.
It's an extremely dense
fog, from the point
of view of the radiation.
And that is what is supposed
to exist below this gray sheet.
The gray sheet is supposed
to be an equal-time surface,
representing the time
of recombination,
that is the time when
matter became neutral.
By the way, this has always
been called recombination.
I don't think
anybody really knows
why the prefix "re" is there.
But this is when
protons and electrons
combined to form neutral atoms.
Beyond that,
suddenly the universe
becomes very transparent.
Neutral gas is very
transparent to radiation.
So we believe that the photons
that we are looking at now,
coming back from along
that past light cone,
were less scattered where
they intersected this sheet
at the time of recombination.
And this circle,
which would really
be the surface of
a sphere, if I drew
a full three-dimensional
model, this circle is called
the surface of last scattering,
the last time this radiation
was scattered before
the photons set off
on their very long
journey, which we believe
was uninterrupted from
then until it is now
being received by
the COBE satellite,
right where my red dot
is currently pointing.
Next transparency.
Now, what does inflation
have to do with these density
fluctuations?
Well, at first it appeared
as if the inflationary model
might give a completely
uniform universe,
with no nonuniformities
whatever.
And that would, of course,
be at odds with our universe.
These nonuniformities,
that COBE is detecting,
we believe are associated with
ripples in the energy density
in the early universe,
which are in turn associated
with the subsequent
formation of galaxies,
clusters of galaxies, and so on.
The key point is
that the universe
is gravitationally unstable.
If there's any
slight excess of mass
in some region of the
universe, that will, of course,
create a slightly
stronger than average
gravitational field, which
will in turn pull more mass in,
creating a stronger
gravitational field.
And the process will
cascade until one develops
the complicated structure
of galaxies and clusters
that we observe in
the universe today.
But in order to
start it all off,
one does need to have
small nonuniformities
in the initial mass density
distribution or else
no structure forms.
Now, as I said, the
inflationary model,
when one first thinks
about it, appears
to give a completely
uniform universe.
Because what you
have is this energy
density of the
false vacuum, which
is just fixed by
the Lagrangian that
describes the false vacuum.
And it would be the
same at all places,
giving you a
featureless universe.
This was a topic that was much
discussed back in 1982, shortly
after the invention of the new
inflationary model by Linde,
and Albrecht, and Steinhardt,
which brought new interest
to the idea of inflation.
It was finally realized-- and
I'm pretty sure it was Stephen
Hawking who first
pointed this out--
that since the world is
really quantum mechanical,
this classical
prediction of inflation
is clearly not the final answer.
In a quantum mechanical
world, any classical statement
is, of course,
really just the peak
of a quantum mechanical
probability distribution.
So if classical
physics, plus inflation,
predicts a completely
uniform universe,
one would assume
that quantum physics,
plus an inflationary
model, would give you
small deviations about
that uniform mass density.
And perhaps these could be the
seeds for galaxy formation.
There was then a complicated
series of interchanges.
Stephen Hawking, himself,
wrote a paper about this,
claiming that everything
worked exactly right.
And that you even got the right
amplitude for the fluctuations,
as well as a spectrum that
cosmologists had thought
was very plausible.
Then a number of the rest of
us started thinking about it.
And we didn't understand
Stephen's calculation.
And we eventually were able
to do our own calculations,
and got an answer that was
very different from Stephen's.
The answer we got
was the spectrum
was what Stephen had said,
which was a desirable result.
But that the amplitude that
we would get would be about 10
to the 5 times
larger than what one
actually wanted for
galaxy formation.
And that was, of course,
very disappointing.
This whole issue came to a
head in the summer of 1982,
when there was a
conference in Cambridge,
England, which was organized
by Gibbons and Hawking,
called the Nuffield Workshop
on the Early Universe.
And about six people
or so, they were
working on this problem
of density fluctuations
in the early universe.
And we were all disagreeing
with each other all
during the conference.
But by the end of
the conference,
we actually did
settle our differences
and come to an agreement
on what the answer is.
And that agreement
has stuck ever since.
And the answer turned out to be
not the one that Hawking got,
but the other one, the one
that gave a number that was 10
to the 5 times too large.
Now, what's also true,
though, which is crucial here,
is that the amplitude of
these fluctuations, it
turns out to be very
model dependent, very
much dependent on the
underlying particle physics
that one assumes.
And we were all
working in the context,
at this point, of the minimal
SU(5) grand unified theory,
which at that point was far
and away the most popular idea
in grand unified theories.
And we realized that if that
model were not the case,
it would be possible to get
any amplitude we wanted,
including, of course,
the right amplitude.
So we were spending
the next few years
hoping that the minimal
SU(5) grand unified
theory would go away.
Our hopes were fulfilled.
Due to the marvelous
proton decay experiments,
it was found that the prediction
that these models made
for the proton
decay lifetime were
inconsistent with observation.
And, in fact, now
nobody knows what
the correct grand unified
theory is, if indeed any of them
are correct.
So what can be said presently
is that the spectrum predicted
by inflation is
about what one wants.
And the amplitude is
adjustable, depending
on what elementary particle
physics one puts in
to underlie the inflation.
What I now to
describe briefly is
how one calculates density
fluctuations in these models,
where they really come from.
In an inflationary model, the
scale factor driving inflation
expands exponentially.
The Hubble constant, which turns
out to be just R dot over R,
is at a constant, chi, the
exponential expansion rate.
This is to be contrasted with
a radiation-dominated universe,
in which the scale factor grows
like the square root of time.
And the Hubble constant
then falls, like 1 over 2 t.
Try to remember these equations
for the next transparency.
Next transparency.
This diagram is more or less
crucial to understanding
just the kinematics of how
density perturbations evolve,
which is all I'll
try to explain today.
First, let's look at the line
that my red pointer is now
pointing to, which is the
inverse Hubble constant.
During the inflationary
era, that's constant.
At the end of inflation,
the Hubble constant
falls like 1 over t.
So the inverse Hubble
constant grows like t.
So the line goes like this.
Now, the relevance of the
inverse Hubble constant
is that it sets the effective
scale at which different things
can influence each other.
If two objects in the
universe are separated
by the inverse
Hubble constant, it
means that H times
the distance is 1.
It means that
they're moving apart
from each other at effectively
the speed of light.
So things that are beyond H
inverse from each other cannot
affect each other, while
things that are less can.
So it sets the scale
of causal influence.
The other line
follows the wavelength
of a typical fluctuation.
You follow the
Fourier mode as it
is stretched by the
redshift of the universe.
So the wavelength just follows
the scale factor itself,
which rises exponentially
during inflation.
And then rises like the
square root of time,
thereby turning
over it and allowing
itself to intersect the
Hubble constant curve again.
So it took this course twice.
Our fluctuation starts out very
small compared to H inverse,
then becomes larger
than H inverse,
and then comes back in, inside
the Hubble radius again.
The notion behind
the way fluctuations
arise in inflation is that they
are established at this point.
And then we measure them
after they come back
inside the Hubble length
at much later times.
The fluctuations are caused--
I think I'll skip some
transparencies here
to save time.
But the fluctuations are caused
by the nonuniformity with which
the scalar field rolls down the
hill in the potential energy
diagram.
It's not a classical
process, obviously.
It's a quantum process.
And it is possible to
really calculate the quantum
deviations in the rolling
of the scalar field
down the hill, which leads
effectively to deviations,
small deviations, in the
time at which inflation
ends at different places.
And one can trace
this through using
a linearized approximation
of general relativity
to actually calculate
then what are the density
perturbations predicted today.
And then I guess-- why
don't you just flash
the next few transparencies.
I can tell you how many to skip.
Audience, don't look.
You're not supposed to
be bothered with these.
Okay, next one.
[LAUGH]
One more.
Hold the next one.
This is the prediction.
The prediction is that if
you measure a Fourier mode--
so it's a function of k, of
the perturbation and the mass
density over the mass density,
the fractional perturbation
of the mass density--
at the time when these waves
come back inside the Hubble
lens, at the second
Hubble crossing
in that original
diagram, inflation
predicts that that should
be roughly a constant.
It does depend slightly on the
underlying particle physics.
And if you make the underlying
particle physics very strange,
you can, in fact, make it more
or less anything you want.
But almost all sensible
particle physics
will give you
something here, which
is very nearly a constant.
And that's known as
a Harrison-Zeldovich
or a scale-invariant spectrum.
And the probability distribution
for any given Fourier mode
is completely Gaussian.
This is actually dictated by
just the zero-point quantum
fluctuations of a
quantum field theory.
Next transparency.
Now, we can come to
what COBE has measured
and how to compare it to this.
What COBE has
effectively measured
are the fluctuations
in temperature
as one looks at
different angles,
but with reasonably large
errors on any given pixel
in this picture.
So it's really the
data that you get
by correlating those
pixels that's relevant,
and not the map that you get
of the pixels themselves.
They've measured it in
three different wavelengths,
corresponding to 3.3,
5.7, and 9.5 millimeters.
For safety's sake, they had
two nearly independent channels
at each wavelength.
So they can compare
them with each other.
And having three different
wavelengths, of course,
was also used to
check their data.
Let me point out that when you
look at black-body radiation,
at any given wavelength
the intensity gives you
a measure of the temperature.
It doesn't have to fit the
whole curve to figure out
what the temperature is.
It measures the intensity
of any given wavelength.
And that uniquely
determines the temperature.
So by having three
different wavelengths,
if all three temperature
measurements agree,
they think they can have
confidence in the results.
If they differ, then
they might think
it's an absorption by some
molecule or something.
Those kinds of effects would
be particular to some frequency
or another, and would not give
the same temperature shift
for all three measurements.
The beam size is quite large.
There's a 7 degree
Full-Width-Half-Max.
So COBE is not capable of
seeing the really fine structure
in the cosmic
background radiation.
COBE is only capable of
seeing the very, very
large-scale structure.
In terms of present-day
structures in the universe,
this actually is a
serious limitation.
The clusters and the
galaxies that we see actually
evolved from
perturbations that are too
small to be visible to COBE.
So what COBE is seeing is
the very large wavelength end
of the spectrum
of perturbations.
Perturbations are, in fact,
too large in wavelength
to be directly responsible
for any visible object
in the universe.
They were very careful,
applied a lot of corrections
They even-- this really
kind of amazes me.
This is on the next--
yeah.
They even had to correct for
the effect of the Earth's
magnetic field on
their instruments.
After doing all
their best shielding,
they still found an
effect, which they
could tabulate and correct for.
And when they were done with
all of their subtle corrections,
they obtained--
next transparency-- a
correlation function,
which is the key result
which they've obtained.
It's the expectation value of
the temperature fluctuation
at one point, times the
temperature fluctuation
at another point, at some
particular angle, alpha.
And this quantity is computed
for all pairs of points
on the sky and then averaged
over all pairs of points
at a given value of alpha.
And then that's plotted
as a function of alpha.
So the correlation function
represents the correlations
in the fluctuations at
a particular angular
separation between
the two points
that are being
looked at on the sky.
The results are on
the next transparency.
These are the results.
Error bars are shown.
The error bars are
intended to include
both systematic and
statistical errors.
If the COBE people are
right, once they've
refined their data correcting
for systematics the way they
have, they believe that most of
the residual error is, in fact,
statistical.
But, of course, there's
always the possibility
of somebody discovering
a systematic error
that they missed.
The gray band-- and this is
what's so beautiful to people
who have been working on this--
the gray band represents
the prediction
of this scale-invariant
Harrison-Zeldovich spectrum,
predicted by inflation.
The reason it is a
band and not a line
is that the prediction is,
after all, probabilistic.
What we are seeing here is
directly the implications
of quantum mechanics.
This is a real quantum
mechanical experiment,
if our underlying
theory is right.
So naturally one does not
make a precise prediction.
But rather, what is
predicted by the theory
is a probability distribution.
And the gray band is the
result of Monte-Carlo studies
of that probability distribution
and represents a 68% confidence
level of the distribution.
They fit this to
a power law to see
how well they could
determine this
to be a scale-variant spectra.
And, unfortunately, the error
bars are still pretty large.
They fit it to a power
spectrum, where n equals 1.
The way they've defined things
is the scale-invariant spectrum
that's being predicted.
And what they find when
they do a fit to the data
is that they get an n of
1.1, plus or minus 0.5.
So it's the right answer.
But the error bars
are too large.
So they have to keep working.
And they will.
COBE is still in the air.
They have another
year's worth of data,
which they have yet to analyze,
which they certainly will.
And they are still in the
air, gathering more data.
And hopefully, before
it's over, they
might have as much as
four years' worth of data.
And the errors should
come down considerably.
Next transparency.
They also were able
to do another test.
What they measure is the very
long wavelength fluctuations.
But we have some idea what
the shorter wavelengths
fluctuations are from
theories of galaxy formation.
Those are uncertain by
maybe a factor of two.
But because they're on
such shorter wavelengths,
it still gives you
a good handle we're
trying to extrapolate
a slope to determine
the variation of the
spectrum with wavelength.
So by doing that, and allowing
for this uncertainty of about
a factor of two in the
amplitude at small values
of the wavelength, they
were able to attain
an alternate value of n, which
I believe is actually completely
independent of the first one.
The first one depends on
the shape of their own data
with wavelength.
This just depends on taking the
normalization from their data
and comparing it with
short wavelength estimates
from galaxy formation.
And what they get this
time is an n which
is also 1; in fact, to
slightly better accuracy,
0.23 this time.
And this is a measurement
which stretches
over three decades of scale.
They also, of course,
have measured a magnitude
to these fluctuations.
They measured the
quadrupole moment,
which corresponds to a
fluctuation in the temperature
of 5 parts in a million.
This exceeds the best previous
bound by about a factor of two,
which is very nice.
The best previous bound being
the result of an MIT balloon
experiment by Stephen Meyer.
They've also fit the results
to an assumed scaling-variant
power spectrum,
finding a delta T
over T, which differs
slightly from what they get
by measuring the quadrupole.
Next transparency.
Now, what are the
implications of this?
Well-- how much
time do I have left?
Good.
By being able to directly see
these primordial fluctuations
in the cosmic
background radiation,
it enables us to ask a question,
which cosmologists have always
wanted to answer,
but have never before
had the ingredients
necessary to answer.
That is, now that we
know how things started,
at least on some lens
scales, we can ask,
do we understand
how the universe
evolved from these early
conditions to the present?
In particular, the
question tends to be,
given these very
small nonuniformities
in the early universe,
can we understand
how the very significant
structures that we
see in the universe evolved?
Well, the answer turns out to
be yes under some assumptions,
and no under others.
And that's very
important because it
helps single out the theories
of structure formation
that have a possibility
of doing the job.
So far, of course, the
choice is by no means unique.
But a number of possibilities
have been ruled out.
In particular, one
rather staggering result,
but which appears to be valid--
I'm sorry.
I have to start the
beginning with a caveat.
The caveat is important.
In order to ask how
structure evolved
from the primordial
fluctuations,
one has to look at the
fluctuations on the same scale
as the structure.
And as I mentioned
earlier, those
are unfortunately not really the
scales that COBE is looking at.
COBE is looking at much
longer wavelengths.
So if one makes
no extrapolations,
and just tries to work with the
raw COBE data as it's measured,
one essentially
has nothing to say
about how a structure
in the universe
could have evolved because those
structures evolved from shorter
wavelength primordial
fluctuations.
So all the implications
really hinge
on being willing to
make the assumption
that the scale-invariant
spectrum which COBE sees
can be extrapolated down
to shorter wavelengths.
And then, looking at
the shorter wavelengths,
one can ask, can we understand
how those very small deviations
in the early universe
evolved to become
the present-day structure?
So everything I
have to say here is
based on that one very
important assumption.
If you make that assumption,
then one immediately
gets a very remarkable
result. All new models
in which the mass density is
dominated by baryonic matter,
matter that's made out
of protons and neutrons,
appear to be ruled out.
The problem is that baryonic
matter couples rather strongly
to photons, right up until the
time that the matter becomes
electrically neutral,
this recombination.
Then it just turns
out there's not
enough time for the
matter to then clump,
if it was that smooth at
the time of recombination.
On the other hand,
in these models
of dark matter, in which
the dark matter is assumed
to be very weakly
interacting, that dark matter
would not be strongly
interacting with the radiation.
And it would start to
clump long before the time
of recombination, giving
itself a head start.
So if the dark matter
theories are right,
the early universe, at the time
that COBE was looking at it,
was not nearly as smooth
as what COBE is seeing.
But COBE is seeing
a very smooth result
because it looks
only at the photons.
While if the dark matter was not
interacting with the photons,
it could have been
significantly more clumped,
and would have been even.
So a strong indication that
what we have in the universe
is some form of
non-baryonic matter.
It's still, of
course, a big mystery
what exactly that matter is
likely to turn out to be.
They also looked at a
number of specific models.
For example, they looked
at cold dark matter models,
both with large Hubble constants
and small Hubble constants.
With a large Hubble constant,
which is what's discussed here,
it does not work.
It turns out that
there's just not
enough time for structure to
form if you start out with a--
I'm sorry.
I got that wrong.
In this model, it actually
works the other way.
With a large Hubble constant,
in a cold dark matter model,
too much structure forms, if one
assumes the initial conditions
as indicated by COBE.
Next transparent-- next
and final transparency.
Listed here are three
models which appear to work.
So, as you see, the field is
not narrowed down very well yet.
What is a very attractive
model to most people
working in theoretical
cosmology is a cold dark matter
model with a low Hubble
constant, a Hubble
constant of 50 in
the astronomers'
units of kilometers per
second for a megaparsec.
This is about a low
a value as can be
tolerated given observations.
And some people will say
it cannot be tolerated.
But some people say
that about everything.
The model gives a very
good fit to structure
on a very wide range of scales.
The only thing in structure
that does not account for
is one observation of
very large structure
on scales of about a
hundred megaparsecs,
seen in a study known
as the APM study.
This has yet to be confirmed.
So it's not that clear if
a correct model should fit.
Many structures have been
seen in the universe,
and have later gotten away
with more careful studies.
There also is perhaps a problem
on very short length scales.
On very short length
scales, the problem
is the calculations become
very hard to do because things
become very non-linear.
But people's best estimates
give a contradiction
on very short length scales.
One possibility
for perhaps healing
the disagreements of this
model would be if one believes,
and one does have some
reason to believe,
that there might be
light neutrinos in, say,
the seven-electron volt range.
Such a neutrino would not
dominate the dark matter
of the universe.
It would not be the dark matter.
The dark matter
would have to still
be some other slowly moving,
weakly interacting particle,
known generically
as cold dark matter.
But a mixture of neutrinos
would, of course,
give you an extra parameter.
And it works exactly
in the direction that
would allow you to give
more power at large scales,
and less power at
small scales, which
seems to be what the
astronomical observations are
pointing towards.
So this model is still probably
the favorite of most model
builders in cosmology.
But several other
models remain open.
In particular, number
five here, in open model,
therefore inconsistent
with inflation.
But an open model is,
nonetheless, apparently
consistent with COBE.
However, it cannot be an open
model in which all the matter
is baryonic.
It's not the simple
universe that some people
have advocated.
It's still a universe in which
more than half of the matter
is non-baryonic.
It's the only way
you can get initially
small density fluctuations
to grow large enough.
And, finally, what
also works quite well,
but most particle theorists
regard this as distasteful,
there is the possibility of
having a cosmological constant,
which makes up most
of the effective mass
density of the universe.
It's sometimes
called vacuum energy.
And that does fit the data.
Although most theorists
regard it as implausible
that the cosmological
constant should just
happen to have a value which is
relevant to cosmology, picking
up, in particle
physics terms, what
represents energy of the vacuum,
which may not have anything
to do with the cosmology.
So as you see, the results of
COBE are extremely exciting.
And what I think is
the most exciting thing
is that it's by
no means finished.
If COBE is right, a number of
ground-based, balloon-based
experiments are
just on the verge
of seeing nonuniformities on
the cosmic background radiation.
And these, in fact,
will give us information
on the very interesting
smaller scales, the scales
which really are the
scales from which galaxies
and clusters of galaxies form.
And the COBE satellite
itself, will be also
giving us more data.
And since most of the errors
appear to be statistical,
the error bars on
the COBE data will
come down very significantly
over the next years.
So what COBE has done, I
think, is to really open
a new era in astronomy.
We now have a new
form of astronomy,
the astronomy of the
fluctuations of the microwave
background.
And it has the
possibility of telling us
a really large amount of
information about exactly
how our universe evolved.
Thank you.
[APPLAUSE]
