[MUSIC PLAYING]
GUTH: I brought
along Snoopy thinking
about my favorite equation.
By the end of
today's talk, if you
don't recognize that equation,
you'll know what it means.
I got into this business
of the early universe
starting out as a
particle theorist.
In about 1978, I and
a reasonable number
of particle theorists began to
dabble in the early universe.
A lot of our
colleagues, at the time,
felt that we were
motivated mainly
by jealousy of Carl Sagan.
But I hope to make it
clear during today's talk
that there were also some
motivations which came directly
from what was going on in
particle physics itself.
What I have in
mind is the advent
of grand unified theories.
And to explain that, I'd like
to give you a capsule summary
history of what was going on in
particle physics over that time
period.
When I was a graduate student
back in the late 1960s,
it was a period that,
looking back on it now,
really looks like the Dark Ages.
At that time, we only
really understood
one interaction of nature--
electromagnetism.
The theory of quantum
electrodynamics
had been more or less
developed since the late '50s,
and that theory
seemed to provide a,
as far as we could tell,
perfect explanation
of electromagnetic phenomena.
But there are three
other known types
of interactions in nature--
the weak interactions, the
strong interactions, and also
gravitation.
And those interactions were
really not understood at all.
However, the early '70s were a
period of tremendous progress
in particle physics.
The work of Glashow,
Weinberg, and Salam
was synthesized to
provide a unified model
of the weak and
electromagnetic interactions.
And as far as we
can tell, that model
works perfectly to
describe those phenomena.
At about the same
time, the theory
of quantum
chromodynamics, QCD, was
developed to describe the theory
of the strong interactions
as a theory of
interacting corks.
And as far as we can
tell, that theory
also provides a perfect
description of the phenomenon
that it was intended
to describe.
So we very suddenly
went from a period
where we understood only one
out of the four interactions
of nature to a period where we
think we understood three out
of four interactions of nature.
That led to an
atmosphere of euphoria,
really, among the particle
physics community.
And there was a
very strong desire
to move further, to try
to develop theories that
would describe
phenomena not yet found,
phenomena beyond the
range of our accelerators.
And the guiding word
behind that movement
was unification, the idea
that it would be much more
attractive to have a simpler
theory where there was one
fundamental interaction to
replace these three that we
understood.
Gravity, all this time,
was left along the side.
Gravity at the
quantum level only
becomes important at
much higher energies.
So it's safe, in a preliminary
way, to leave gravity out.
However, at the energies
at which we do experiments,
the strong interactions
are really quite
a bit different from the
weak and electromagnetic
interactions.
And what that meant
was that in order
to build a unified
theory, it was necessary
that the unification
occur at an energy which
is very far removed
from the energies
at which we do experiments.
And that's what led to
this fantastic energy
scale of about 10
to the 14 GeV, which
is a characteristic energy
scale of these grand unified
theories.
Now, 10 to the 14 GeV, that's
about three orders of magnitude
beyond what Ken was
talking about in his last
talk at the beginning.
It's about the energy it takes
to light a 100-watt light
bulb for a minute, which
doesn't sound like that much.
But again, to have
that much energy
on a single elementary particle
is genuinely extraordinary.
One way of seeing how
extraordinary it is
is to try to imagine
building an accelerator
to reach 10 to 14 GeV.
In principle, you can do
that by building a very long,
linear accelerator.
The energy of a
linear accelerator
is just proportional
to its length.
So it's an easy
calculation, at least,
to figure out how long the
accelerator would have to be.
And it turns out that,
using present technology,
the length of the
accelerator would
have to be almost
exactly one light year.
Now, it seems unlikely
that such an accelerator
would be funded in the days
of the Gramm-Rudman Amendment.
So what that means is that if
we particle theorists wanted
to try to see the dramatic
10 to the 14 GeV scale
consequences of these
grand unified theories,
we were forced to turn to the
only accelerator to which we
have any access at all which
has ever reached those energies,
and that appears to
be the universe itself
in its very infancy.
According to standard
cosmology, the universe
would have had a temperature
with KT equal to 10 to the 14
GeV at a time of about 10
to the minus 35 seconds
after the Big Bang.
So that is the real impetus
for particle theorists
to dabble in the early universe.
Now, what I want
to talk about today
is a scenario called the
inflationary universe,
and I'll get there towards
the end of my talk.
If time permits,
there's a little bit
of new material, which I may
or may not get to discuss.
I want to begin,
though, with basics.
I'd like to begin by reviewing
the standard cosmological
scenario.
That is, without inflation.
So that I can point out
what defects of this model
the inflationary model
was designed to solve.
Now, the standard
cosmological scenario
is something that I
learned about in a course
that I took as a
graduate student
once at MIT, a course that
was taught jointly by Phil
Morrison and Steve Weinberg.
I don't remember how
well I did in the course.
So if I get any of this
wrong, it could either
mean that I botched it or it may
have been one of the lectures
that Steve gave.
But in any case, we can get
it all straightened out,
because my teacher is here
to answer any questions.
The standard scenario is
based on several assumptions,
the first of which is
that the universe is
homogeneous and isotropic.
The universe certainly
appears to be
homogeneous and isotropic.
The evidence is, of course,
not absolutely compelling.
But the assumption that's
put into this model
to make it simple is that
the universe is completely
homogeneous and isotropic.
The second assumption,
which has to do
with describing the
early universe, which
is all I'm going to
be speaking about,
was that the mass density
of the early universe
was dominated by the black body
radiation of particles which
were effectively massless.
By effectively
massless, I simply
mean that their mc squared
was small compared to KT
so that the masses
were negligible.
Third assumption is that
the expansion is adiabatic.
That is, no significant
entropy is produced
as the universe expands.
The universe essentially
remains in thermal equilibrium.
Fourth assumption is that we
understand the laws of physics,
that general relativity
governs the gravitational field
and the large-scale structure.
And the small-scale physics is
just dictated by the physics
that we know about how particles
behave at high temperatures.
When all this is
put together, it
leads to a very simple
picture of the early universe.
It leads to a model
which you can calculate
everything you want to know.
The temperature falls like
1 over the square root
of the time variable.
The scale factor describing
the overall length scale
of the universe grows
like the square root
of the time variable.
And just to give you
some sample numbers that
are relevant to people like me,
who are interested in applying
grand unified theories
to the early universe,
if we look at the time when
KT was 10 to the 14 GeV,
the temperature
scale of interest,
it happened at a time of about
10 to the minus 35 seconds,
as I guess I've
already mentioned.
The mass density
at that time was
a colossal 10 to the 75
grams per centimeter cubed.
That's the kind
number that nobody
would have dared speak about
when I was a graduate student.
Let me remind you that the
density of an atomic nucleus,
which was about the densest
thing anybody would dare talk
about when I was a graduate
student, is only about 10
to the 15 in these units.
So we're up another 60
orders of magnitude.
The size of the region
that will evolve
to become the observed
universe at that time
was about 10 centimeters.
Now that, of course,
should not be
confused with the size
of the entire universe.
We have no idea what the size
of the entire universe is.
It can be arbitrarily
larger than 10 centimeters.
Now, even though I'm
going to be proposing
a modification of
this model, I do
want to point out
that the model has
some very important successes.
And when we talk about
modifying the standard model,
it's, of course, also
important to make sure
that you modify it in a way
which maintains the successes
that the original model had.
One important success is
that the standard model
explains Hubble's law.
If you have a uniform system
which uniformly expands,
if you work out a little
bit of arithmetic,
you see that Hubble's law
immediately falls out.
You get a velocity which is
proportional to the distance
to any given object.
The second important
success, which has already
been discussed in
Jim Peebles' talk,
is that this model explains the
cosmic background radiation.
Because obviously, if the
universe is expanding,
it means it's also cooling.
The early universe would,
therefore, have been very hot.
And there would be
thermal radiation leftover
from this initial hot period.
Finally, as Jim Peebles also
discussed in much more detail,
the model gives rather
successful predictions
for the abundances of
the light elements.
You have a detailed
scenario that tells you
how the universe
cooled, which means
that if you know
particle reaction rates,
you can actually
compute how many
of the different kinds of nuclei
should have been produced.
And there is one important
unknown parameter
in that calculation,
and that is the ratio
of baryons to photons.
But you have a number of
things you can calculate.
And the fact of the matter is
that for a reasonable value
of this unknown parameter, you
can fit these various pieces
of data quite well.
So that is, in
addition, a rather,
I think, spectacular success
of the standard model.
However, I want to
point out that all
of the successes of
the standard model
only pertain to the behavior
of the model at times
after about one second
after the Big Bang.
We really have no
direct evidence
that the standard model
is valid at earlier times.
So the inflationary model
will make use of that fact,
and it will modify the
standard scenario only
at times which are, in fact,
much earlier than one second.
Okay, let me speak
next about the problems
of standard cosmology that
the inflationary model was
intended to solve.
I want a list four of them.
The first is probably the best
known, the horizon/homogeneity
problem.
It has to do with the fact
that this cosmic background
radiation has been very
carefully observed.
And it's known to have
the same temperature
in all different
parts of the sky
to an accuracy of better
than one part in 10 to the 4.
Now, normally, when
you discover an object
with a uniform temperature,
you can tell yourself
that's easy to explain.
If you let a glass of water
sit on the table long enough,
it will come to a
uniform temperature.
But in the context of
this standard cosmology,
that absolutely cannot happen
for the early universe.
There just is not enough time.
One way of phrasing it is
you can imagine, regardless
of what physical processes
were actually taking place,
you can imagine you had a
network of little green men
scattered around the universe
whose mission was to arrange
for a uniform temperature.
And they have little ovens,
so they can heat things up
when they wanted to and little
air conditioners to cool things
down when they wanted to.
But they can only
communicate with each other
at a fixed speed.
And what's easy to calculate
is that in order for them
to achieve this
feat of arranging
for the cosmic
background radiation
to have a uniform
temperature, they
would have to be able to
communicate with each other
at more than 90 times
the speed of light.
And that is what's called
the horizon problem.
There just isn't enough
time for the communication
to take place.
Now, this is not a
genuine, absolute flaw
in the standard model.
The standard model still works.
You simply have to assume
in your initial conditions
that the temperature was
uniform at the start,
and then the universe
will continue
to evolve with the
uniform temperature.
But what it is is a serious
lack of predictive power
of the standard model.
This very dramatic
feature of the universe,
this incredible uniform
temperature throughout,
has to simply be postulated.
It could in no way be
predicted or calculated
on the basis of
standard cosmology.
And that's the
horizon/homogeneity problem.
The flatness problem has
to do with the mass density
of the universe.
And I want to speak about the
quantity which everybody calls
omega, which is the
ratio of the actual mass
density to the
critical mass density.
Now, we still don't
know very accurately
where omega is today.
It's somewhere
between 0.1 and 2.
I think many observers
would like to put--
would estimate much tighter
constraints than that.
But I won't argue with them.
I'll just say that,
okay, you agree with me
it's somewhere
between 0.1 and 2.
I'm not worry about where
within that range it might be.
The point is that omega equals
one is an unstable equilibrium
point of the standard
model evolution.
That means if omega's
exactly equal to one,
it will remain
exactly one forever.
But if it's a little
bit off from one,
it will immediately start
to move in that direction.
So it's like a pencil
standing on end.
So to be anywhere near omega
equals one today, which
is a very late time in the
history of the universe,
it means that at
much earlier times,
omega must have been
very much closer to one.
And in particular,
if you go back
to one second,
which is not really
an extraordinary
time in cosmology--
it's the beginning of the
nucleosynthesis processes.
At that time, omega had
to have been equal to one
to an extraordinary accuracy
of one part in 10 to the 15
in order for us to be
where we are today.
So what that means is that in
standard cosmology, at whatever
time you want to start the
universe-- if you want to start
it earlier than one
second, you have
to postulate omega was
even closer to 1 than that.
Whatever time you
start the universe,
you have to postulate
that omega at that time
was extraordinarily
close to one in order
for the subsequent evolution
to agree with what we observe.
As far as I know, this
was first pointed out
as a problem in a paper
by Dickey and Peebles,
which I guess came
out in 1979, I think.
It's a fairly
recent consideration
that this should be
regarded as a problem.
Although, I should add that
the basic facts here, I'm sure,
were known since the time
of Friedman in the 1920s.
The third problem I
want to discuss I'll
call the density
fluctuation problem.
The point is that
although you want
to arrange for the
universe to be homogeneous
on very large scales,
on smaller scales,
there's certainly
inhomogeneities
that we observe--
galaxies, stars, clusters,
this hotel, and so on.
And in order for that
structure to form,
there has to be seeds
in the early universe.
If you start completely
uniform, the universe
will simply evolve and
remain completely uniform.
In the standard
cosmology, there's
absolutely no trace of a
clue as what the seeds are
that form the galaxies.
One simply has to put
in a primordial spectrum
of fluctuations in order
to make the model work.
So again, essentially, all
the important properties
of the universe
simply have to be
put into this model
as assumptions
about the initial conditions.
Finally, I move on to what
I'm calling problem four,
the magnetic monopole problem.
Of these four problems,
this is the only one
which is not a problem
of cosmology by itself.
This is a problem
that only arises
when you try to
combine cosmology
with these grand
unified theories.
The grand unified
theories predict
that there should
be particles, which
are magnetic
monopoles, that have
extraordinary masses,
masses of about 10
to the 16 times the
mass of a proton.
And given the standard
cosmology and particle physics,
you can try to estimate how
many magnetic monopoles would
have been produced in
the early universe.
And the conclusion
that you come to
is that far too many
magnetic monopoles
would have been produced.
So some modification has
to be found somewhere
to suppress this production
of magnetic monopoles.
That ends my summary
of standard cosmology.
What I want to do next is
to describe some properties
of the vacuum,
because it turns out
that understanding
the vacuum really
gives you all the
physics that you
need to understand inflation.
The vacuum used to be simple.
Back in the old
days, the vacuum just
meant the absence of anything.
And nothing could be
simpler than that.
Modern physics has
changed all that.
The vacuum is now about the
most complicated structure
that we know of, and
I'll elaborate on that.
The dictionary
definition is something
like the absence of matter
or space empty of matter.
But that never really was
the physicist's definition.
The physicist's definition is
one which obviously at least
allows for complexity.
The physicist's
definition of the vacuum
is simply given
your theory of what
describes the universe, what
is the state of lowest energy
of that theory?
That is what we call the vacuum.
And it may be simple if
you have a simple theory
like Newtonian mechanics.
The state of lowest
energy is just
to take away all the particles.
And then you have a very simple
description of the vacuum.
But in more
complicated theories,
the state of lowest
energy, obviously,
has the possibility of
becoming more complicated.
And that is what happens.
The vacuum started to become
complicated, at least so
far as I know, with the advent
of quantum electrodynamics.
In quantum
electrodynamics, there
are two things that make
the vacuum complicated.
First of all, you have
the electromagnetic field.
And the electromagnetic field,
in quantum electrodynamics,
is constantly fluctuating.
The reason is basically
that you calculate this
by decomposing the
electromagnetic field
into a series of standing waves.
Each standing wave acts exactly
like a harmonic oscillator.
And as you know from
quantum mechanics,
the ground state of
a harmonic oscillator
is not at zero energy.
It's one half h bar omega.
So for each possible
standing wave
of the electromagnetic
field, you
get a contribution of
one half h bar omega
to the energy density
of the vacuum.
How many standing
waves are there?
Well, there's no
maximum wavelength
if you have a cavity
and just talk about what
goes on in that cavity, but
there's no minimum wavelength.
So you have an infinite number
of possible standing waves,
an infinite number of
contributions of one half h bar
omega.
The energy density contributed
by the zero point fluctuations
is infinite.
So the vacuum is not
only complicated,
it already has
divergence problems.
This infinity of
the energy density
is eliminated in
the theory simply
by crossing it off your paper.
You tell yourself that
the zero point of energy
is not really relevant
to this theory, anyway.
You can always
redefine the zero point
at this level of
theoretical development.
It only becomes a problem
once you couple in gravity.
So the energy density
is simply redefined
so that the vacuum has
zero energy density.
However, that's not
the only complication.
In addition to the fluctuations
of the electromagnetic field,
there are also fluctuations
of the electron field, which
one can describe as the
appearance and disappearance
of electron/positron pairs.
And since they appear
and disappear rapidly,
they're given the name
virtual particles.
And these give rise to very
real and measurable effects,
effects which go by the
name of vacuum polarization.
The vacuum can
actually be polarized
by an electric field
because of the appearance
of these
electron/positron pairs.
And that is a very measurable
and very real effect.
Vacuum polarization
also gives rise
to infinities when
you calculate it.
It turns out, though,
that all of the infinities
that the theory producers can
be absorbed into re-definitions
of the fundamental constants.
Of course, they're
re-definitions
by infinite factors.
But once you do
these re-definitions,
then the theory becomes finite.
And that process is
called re-normalization,
and it's a process
which is very, very
important in our understanding
of particle theory today.
Now, all this has a
connection to cosmology
through the
cosmological constant.
It was, as far as I know,
Zel'dovich that who first
realized that Einstein's
cosmological constant can be
interpreted as nothing more
nor less than a energy density
attributed to the vacuum, where
the two are related by this
formula.
Now, if you take
the empirical limit
on the cosmological
constant then translate that
into an energy density, you get
a number of about two times 10
to the minus 8 ergs per
centimeter cubed, it should be.
Sorry about the cube.
Don't have a pen here.
2 times 10 to the minus
8 ergs per centimeter
cubed for our bound on the
energy density of the vacuum.
Now, actually, Zel'dovich,
in his '68 paper,
suggested that
there may, in fact,
be a non-zero contribution
to the energy density
of the vacuum coming
from the QED vacuum.
Now, in order to
make that work, it's
actually very hard, at least
from a modern point of view.
If there was to
be a contribution,
you can try to estimate
by dimensional analysis
how large it would be.
And this is a very
interesting calculation,
which gives what
originally, at least,
was a very surprising answer.
Now it's known to all
particle theorists, at least.
Just using dimensional
analysis, the theory really only
has one characteristic
energy scale,
and that's the mass of an
electron times c squared,
which comes to about eight
times 10 to the minus 7 ergs.
The theory also really only
has one characteristic length
scale, which is the
Compton wavelength
of an electron,
which is 3.9 times 10
to the minus 11 centimeters.
So if you try to make something
with the units of an energy
density, you really
only have one choice.
You take that energy
divided by that length cube,
and you get a number of
about 10 to the 25 ergs
per centimeter
cubed, a number which
is absolutely huge compared
to the bound that you have.
So if there was some context
in which this calculation made
sense, you would
have gotten an answer
that's obviously wrong by
a factor of 10 to the 33.
So clearly, what's going
on is that something
is preventing these
kinds of mechanisms
from contributing to
the vacuum energy,
to the vacuum energy
that we actually measure.
Nobody really knows
what that mechanism is,
and that's really the important
point I want to make here.
In the context of QED, most
modern particle theorists
would have expected
an energy density
to the vacuum of that order.
The actual number is much,
much smaller than that,
and we just do not
understand why.
The situation gets
even more complicated
when we go beyond QED
to more modern additions
to our theoretical arsenal.
The next important
addition, and it really
is a qualitative addition,
is the development
of the
Glashow-Weinberg-Salam model
of the weak and
electromagnetic interactions.
This is what is called the
spontaneously broken gauge
theory.
It turns out that the
only way that we were able
to think of-- or not we, they.
Steve and Shelly and Abdus.
The only way they
were able to think
of to build a finite theory
of the weak interactions,
a normalizable theory of
the weak interactions,
was to combine it with the
electromagnetic interactions
and to incorporate in the
model at the fundamental level
a very deep symmetry
which would cancel
some of the infinities that
would otherwise crop up.
This symmetry, though,
is not a symmetry
which we observe in nature.
If the symmetry
were manifest, it
would say that the mass
of the W and Z particles
would have to be the same
as the mass of a photon.
That is, massless.
They're not.
The W weighs 80 GeV.
The Z particle weighs 90 GeV.
That's what makes the weak
interactions, in fact, weak.
Furthermore, if this symmetry
were exact in nature,
it would say that
an electron would
be indistinguishable
from a neutrino, also
a massless particle.
We know an electron
is not massless.
So the symmetry, which is
the fundamental symmetry
of the Lagrangian of the
theory, the fundamental symmetry
of the Hamiltonian
of the theory,
must not be a
symmetry of nature.
And that's accomplished
by a technique called
spontaneous symmetry
breaking, it's
done by introducing a
new kind of scalar field,
something called a Higgs field.
In this particular theory,
the Higgs field actually
consists of a complex
doublet, two fields, phi one
and phi two, each of
which are complex numbers.
But these are scalar fields.
There's a good
reason why you have
to use scalar fields to
break these symmetries.
Because what we're going to
arrange is for these fields
to have a non-zero
value in the vacuum.
If something like a vector
field had a non-zero value,
that would pick out
a direction in space
and break rotational invariance.
Since rotational invariance, we
know, is a very good symmetry
of nature, if we want
to break symmetries,
we have to use scalar fields.
And the name of the scalar
field that does that
is called the Higgs field.
And it's done by arranging
for the energy density
in the theory, as a function
of the value of the field,
to be a curve that looks
something like this.
Now, the energy
density only depends
on the sum of the absolute
squares of these two fields.
That's imposed by the symmetry.
The symmetry says it can't
depend just on phi one
and not phi two.
It has to depend
on it the same way.
It has to depend, in fact, on
precisely this rotationally
invariant combination
of phi one and phi two.
But what you do is
you arrange-- and you
have some freedom about this.
The theory allows you to
adjust parameters that control
this potential energy function.
And you adjust the parameters
so that the minimum
occurs not at zero, but
it's a non-zero value.
Now, this immediately
means that the state
of minimum energy, the
vacuum, is no longer unique.
Because you can
minimize this curve
by letting the real
part of phi one
have a value of 250 GeV
and all the other zero.
Or you could minimize
this curve by letting
the imaginary part of phi
two have a value of 250 GeV
and everything else zero.
Or an infinite number of
linear combinations in between.
So there are many
vacua, and what
happens in this
theory is that very
early in the history of
the universe, at about 10
to the minus 11
seconds, the universe
settles into one of these vacua.
And the choice that the
universe makes at that time
is the choice which
breaks the symmetry.
Once, say, the real
part of phi one
acquires a non-zero value
when the others are all zero,
that now breaks the symmetry.
You no longer have a
symmetry between rotations
in phi one and phi two.
And that's exactly how the
spontaneous symmetry breaking
works.
And that's the entire purpose
of having this field in theory
in the first place.
Now, you can estimate how
much energy is involved here.
I've drawn this curve the
way it's usually drawn--
contrived so that
the zero point--
excuse me.
Contrived so that the minimum
lies at zero energy density.
But the theory does
not impose that.
You do that by adding
an arbitrary constant
to the energy.
Once again, the real zero of
energy is not really defined.
It doesn't become defined until
you actually have a theory that
couples to gravity.
But if you were to estimate
the characteristic energy
scale that's involved here,
how high, for example, do
you expect the energy
density to be here?
And therefore, how
precisely did you
have to fine tune things for
it to be exactly zero there?
The characteristic
scale is taken
by taking the same formula
we used for quantum
electrodynamics, where we had
the mass of an electron here,
and replacing it with the
mass of the W particle,
the characteristic particle
of the Weinberg-Salam model.
That has an mc
squared of 80 GeV.
And when you put it in, you
get a number that's about 10
to the 45 ergs per
centimeter cubed.
So now we're too high compared
to the observational limits
on the cosmological constant
by a colossal factor of 10
to the 53.
We're not finished yet.
The next important
development is
one that really highlights
the inflationary scenario--
grand unified theories.
In grand unified
theories, you have
a repeat of the same story.
But you have to add a
much higher mass Higgs
field, a Higgs field with
the mass on the order of 10
to the 14 GeV.
And when you plug that in to
find the characteristic energy
scale that you'd
expect to be developed
by this theory as a contribution
to the vacuum energy,
you get a number which
is too high by 108
orders of magnitude.
We're still not finished.
I should mention here
that we're finished as far
as what we need to
know for inflation,
so everything that comes from
here on in is sort of trimming.
And I should also
mention I don't really
understand what comes in
from here on in, either.
But I'll give you
a brief summary.
The next most sophisticated
level of theory
is super gravity.
And the idea of super gravity
is that the fundamental scale
is the scale of gravity
itself, the scale you make out
of Newton's capital G,
known as the Planck mass,
which is 10 to the 19 GeV.
And when you plug that
into our famous formula
here to get converted into a
characteristic energy density,
you get 10 to the 114 ergs per
centimeter cubed, a number that
exceeds the experimental
bound by a full 122
orders of magnitude.
Now we're finished,
as far as I know.
Basically, we're 122
orders of magnitude off.
So what's going on is that
there's some mechanism
that we don't understand
which is suppressing
the cosmological constant by
about 122 orders of magnitude
below what we would
naively expect it to be.
Now I want to comment on
what Jim Peebles mentioned,
that particle
theorists are usually
skeptical about any
notions that there might
be a meaningful
cosmological constant that's
relevant to cosmology.
The argument is, I think,
not a compelling argument,
but there is an argument.
And basically, the way I would
phrase it, it goes like this.
If this unknown mechanism
exists and suppresses the vacuum
energy by 122
orders of magnitude,
it seems highly unlikely
that it stops exactly there.
You would think it would go
for at least another two orders
of magnitude, or
maybe another 10.
And any of those would mean that
the cosmological constant would
be irrelevant.
The only way to get a
relevant cosmological constant
would be for the
suppression to be exactly
by this 122 orders of magnitude,
which just seems unlikely.
Now, as far as how to
rate this argument,
I would say that
it's probably roughly
equivalent to the
theoretical equivalent
to a three-sigma experiment.
As we know with
three-sigma experiments,
you never really know if you
should believe them or not.
Same, I think, with this
theoretical argument.
Now, I want to come to
another concept called
the false vacuum,
which is really
what's going to lead us into the
inflationary scenario itself.
Before, I drew a curve
for the energy density
of a scalar field, which was
on the Higgs field, which
looked like this.
Let's again consider that
we're dealing with the particle
theory, which has in it a scalar
field which behaves this way.
And let's ask ourselves,
what are the possibilities?
When the scalar field
sits on the bottom,
that's the state of
lowest possible energy.
That's what we call, by
definition, the vacuum.
And the word true has
been introduced here just
to be absolutely clear
that that's the vacuum.
However, you can
ask yourself, what
happens if the scalar field
is perched right here, right
on the top of the hill?
Well, if this potential is
quite flat on the top-- which
it can be.
It doesn't have to be.
Then, that state where the
scalar field sits on top
here can be metastable.
That is, it can live for
a certain length of time
before the scalar
field eventually
falls off and rolls down this
hill in the energy density
diagram.
That state where
the scalar field
is in the metastable state
at the top of the hill
is what we call
the false vacuum.
It has an energy density which
is fixed by this curve, which
is in turn fixed by the
parameters of the underlying
particle theory.
And I'll call the energy
density of that state rho sub f.
f for false vacuum.
Let me go on to describe
some of the properties
of this false vacuum.
First, as I mentioned,
the energy density
is fixed, rho sub f.
No matter what you
do to it, you can't
change its energy density.
Because its energy does it
just depends on the fact
that the scalar field is
sitting on top of that hill.
If you move the
scalar field, you
can change the energy density.
But what we're going
to be talking about
is changes which happen too fast
for the scalar field to move.
So we'll consider
the scalar field
to be temporarily
frozen on the top.
And given that, the
energy density is fixed.
Next thing to notice
is that this state
is Lorentz invariant.
That is, if you have
a scalar field which
everywhere in some region
has the same value,
if you were to move
through that region
and measure the
scalar field, there's
no way you can detect your
motion relative to that scalar
field.
You would still find
that every place
where you measure
the scalar field,
it had that value,
electron is zero.
So it's Lorentz invariant.
Motion through the state
cannot be detected.
And that's really the
excuse for calling it
a vacuum in the first place.
False vacua and true vacua are
the only states of nature which
have that property, that you
cannot detect motion through
them.
Finally, and this
is what will really
be important for inflation, the
pressure of this false vacuum
state is negative.
And in fact, it's equal
to minus rho sub f.
