Transcript views of dark energy

VIEWS OF DARK ENERGY
Edward Witten
STScI
May 5, 2008
Regrettably, I don’t have any new concept of
dark energy to explain today.
I just want to explain two not very novel
points:
• Discovery of dark energy greatly changed
how we think about the laws of Nature
• The nature of the change depends
crucially on whether dark energy is a
“cosmological constant”
For me, the discovery of cosmic
acceleration/dark energy was the
most dramatic finding in physics since
perhaps the discovery of the
particle in 1974.
Of course, dark energy has the
somewhat unusual property that it
was a major embarrassment before it
was discovered.
The reason for the embarrassment was
simply that any reasonable calculation of
quantum zero-point energy
gives an answer that is too big by orders of
magnitude – by a lot of orders of
magnitude.
In this formula,
for bosons is
the ground state energy of a harmonic
oscillator mode, where here
And the negative energy
for
fermions comes from filling the Dirac sea.
Bosons and fermions cancel if they have the
same masses … a special case of
supersymmetry.
The formula
is really a one-loop approximation, but
trying to do a more complete calculation
doesn’t seem to help.
The “sum” over states is really
and so is highly divergent.
What answer we get depends on
what we do to cut off the
divergence. However, the
potential error is well over 100
orders of magnitude.
Even with the help of
supersymmetry, one is still off by
about 60 orders of magnitude.
Though there were some dissenters,
the dominant reaction to this was to
expect that somehow it would go
away
… that some very deep and unknown
mechanism, maybe involving
mysteries of quantum gravity, would
one day make the vacuum energy
vanish.
Those of us who thought that way usually
expected that the mystery mechanism
would make the vacuum energy zero (and
not just extraordinarily small) because it
seemed that a value consistent with
observational bounds, but not quite zero,
would be unreasonably small to emerge
spontaneously from a fundamental
calculation.
The discovery of cosmic acceleration seems
to show that the problem is never going to
go away in that sense. But it doesn’t really
prove it, and that is one of the reasons for
the present meeting:
We don’t really know for sure if observed
dark energy is really the energy of the
vacuum or is there because we are not
quite living in the vacuum, as in the
picture:
There is a certain sense, however, in which
the vacuum energy or “cosmological
constant” hypothesis is the minimal one.
This is the only interpretation of dark energy
that is based entirely on General Relativity
with no fields beyond the gravitational
field. One only needs a new constant of
nature:
Every other theory of dark energy needs
new fields (or more exotic new ingredients
of some kind) and a more elaborate
explanation.
This doesn’t necessarily mean that the
cosmological constant is the right theory,
but it is a simple and definite one and
doesn’t yet really have a compelling
competitor; I’ll say more about this at the
end.
To try to give a sense of how cosmic
acceleration has influenced our thinking
about the laws of nature, it is reasonable
to start with the minimal theory, the
interpretation in terms of vacuum energy.
Quantum theory makes it clear that the
“vacuum” that we live in shouldn’t just be
taken for granted as “empty space,” as
pre-quantum physicists probably tended to
do.
The vacuum is filled with “virtual particles,”
and its structure, which results from
solving sophisticated equations of
Quantum Chromodynamics (among other
things) is largely responsible for the way
the world is.
Before the discovery of the dark energy,
quantum physicists tended to assume that
the “vacuum” we live in has some very
deep meaning that reflects Nature’s
deepest secrets.
The discovery of cosmic acceleration has
called this into question since, for one
thing, the period of “inflation” that we are
now apparently entering has an obvious
analogy to the inflation that may have
occurred in the past.
Inflation in the past didn’t go on forever and
maybe that is also the case for the present
epoch of inflation:
We are here!
If this is the right picture, our epoch and the vacuum
we live in seem a little less fundamental!
There is actually something that makes this
picture seem plausible to me.
In the last decade or so, we’ve learned
(through work of Maldacena and others)
that it is definitely possible to make a
stable quantum gravity vacuum of
negative vacuum energy.
Supersymmetrically, zero is also possible.
But it is extremely unclear whether in the
presence of quantum gravity it is possible
to have a stable world of positive vacuum
energy.
If not, the Universe we see must be
unstable, headed for a calamity (possibly
in the very remote future long after all
kinds of more conventional astrophysical
calamities like the collision of the Milky
Way and Andromeda and the burning out
of the stars).
This may seem a little drastic. But actually
in a way it is pretty tame …
The discovery of cosmic acceleration has
motivated, to some, a more radical
reassessment of the role of our “vacuum”:
Us?
What I’ve drawn is usually understood
as a one-dimensional slice of a
complicated multi-dimensional picture!
The idea here is that we shouldn’t aim to
explain why “the vacuum” has a very tiny
energy. Rather, we should look for a
theory that generates all kinds of “vacua”
with different properties – with energy
large or small, positive, negative, or (in the
supersymmetric case) possibly zero.
Such “vacua” are realized in different times
and places in the Universe, perhaps as a
result of cosmic inflation.
According to this picture, we live in a
“vacuum” in which the cosmic acceleration
is small, in part because that is where we
can live.
In this view, the problem isn’t to explain why
our vacuum has a small energy but why
the Universe has all kinds of vacua with
different properties.
This conception has been dubbed the
“multiverse.”
Several distinguished physicists – among
them A. Linde, A. Vilenkin, S. Weinberg,
M. Rees – have proposed or advocated
this picture for years. The motivations
were cosmic inflation, the problem of the
cosmological constant, and curiosity about
whether the Universe could be like that.
String theory wasn’t a primary motivation
at all.
However, taking what we know at face value, string
theory does seem to lead to something like this:
This is actually the main traditional
embarrassment of the subject.
Since I am one of the people who developed
methods to describe approximate string
theory vacua, I am tempted to say that it
was the embarrassment of my youth.
Until about ten years ago, string theorists
generally assumed that we were getting
this sort of result because we didn’t
understand the theory. Who needs that
mess? There is just one world we live in.
But since the dark energy was discovered,
R. Bousso, J. Polchinski, L. Susskind, M.
Douglas and other prominent string
theorists have advocated that this sort of
picture is the correct interpretation of string
theory and the Universe.
I don’t know whether this view will
survive, but I do think that coming to
grips with the cosmological constant –
if that is the right interpretation of
cosmic acceleration – will lead
physicists to think of the “vacuum”
very differently from the way we used
to.
Now I want to go into a little more detail
about the impact of the dark energy
phenomenon on views of string theory.
I’ll summarize the impact in terms of good
news and bad news.
Prior to the dark energy epoch, we assumed
that what we understood was seriously
flawed for two reasons:
One is that there was no explanation for the
vanishing of the cosmological constant.
The other had to do with trying to
understand particle physics.
Though there was no one insuperable
difficulty, and many things even worked
elegantly, it seemed that trying to
understand in string theory the details of
particle physics – the quarks and leptons
and gauge particles, unified with each
other and with gravity – led to a maze of
conceivable choices.
To describe particle physics via string theory,
what one needs is to describe the
“vacuum” of the theory – the observed
particles and forces are then expected to
result from small oscillations around this
vacuum.
There were far too many approximate
vacuum states, and none seemed to solve
the most basic problem of all – vanishing
of the cosmological constant after
supersymmetry breaking.
We assumed – or at least I assumed – that
for the theory to be right, one day a
miraculous new idea would have to solve
these problems.
Making the cosmological constant vanish
would be a key test of this new idea.
And until it was found, our approximate
string theory “vacua” could only be crude
approximations.
The good news then is that if we are really
living in a “multiverse,” it may be that the
theory as we know it is pretty close to the
truth.
If the “Universe” is really a “Multiverse,”
finding the vacuum state we observe
should be like searching for a needle in a
haystack.
But this comes with a hefty dose of bad
news … If the vacuum of the real world
is really a needle in a haystack, it is hard
to see how we are supposed to be able to
understand it.
In other words, if an unimaginably large
number of approximate “vacuum” states
are realized in different parts of the
Universe, none of them with any special
meaning, and with the details of particle
physics depending on where one happens
to live, then what sort of understanding of
particle physics can we hope to get?
I don’t have an answer to this question, but
in a way the important point for today is
that it is a different question from the ones
we’d ask if we didn’t know about the dark
energy.
Now I move on to the last part of this talk…
A lot of what I’ve said is most natural if we
assume the minimal theory of dark energy
– that is, the cosmological constant.
If the dark energy is something more
complicated, then all bets are off.
For example, dark energy might really
represent the discovery of a new
elementary field or particle.
Here is a picture in which “dark energy” is
really a sign of a new elementary particle:
We are here
There is a stable nonaccelerating vacuum,
but we haven’t reached it yet.
If this is the right interpretation, then all the
new thinking I’ve mentioned that has been
occasioned by the discovery of cosmic
acceleration may be misleading.
There might be, after all, a unique stable
vacuum, with vanishing vacuum energy.
Elementary particle physics might spring
uniquely from the underlying laws of nature,
with uniquely determined values of
dimensionless numbers like
or
All the old viewpoints may be correct.
I have to say that I would be happy if this
turned out to be the case – since I think it
is more interesting if the dark energy isn’t
just a constant, and I wish we would have
a chance to compute one day the
dimensionless constants of nature.
But there definitely are some difficulties.
In a picture like the one shown here, there
should be a “fifth force,” resulting from
couplings to matter
We are here
of the new and necessarily very light scalar field
Although there is no clear problem in
principle, if one tries to make a model like
this in string theory, one soon finds that it
is difficult to get a potential that is flat
enough to account for why our vacuum
seems to be stable, and to make the
scalar interact weakly enough to make the
fifth force weak enough – that is, to
preserve the successes of General
Relativity.
There are lots of relatively light scalar fields - that is where the “landscape” came from
but generally they aren’t really light enough,
and/or they couple too strongly to ordinary
matter.
To me, the version that is closest to working is that
the spin zero field could be one of the “axions” of
string theory, a spin zero field similar to one of
the fields that may be responsible for solving the
“strong CP problem’’ (smallness of neutron
electric dipole moment).
The potential of such a field looks like
with constants
and
.
There are three things one needs to make the
model viable:
The vacuum energy should be suitably small; the
Universe should evolve very slowly; and the
couplings of
to ordinary particles should be
very tiny.
For this,
should be rather close to the
Planch scale and
should be incredibly tiny.
It actually isn’t hard to satisfy either one of these
conditions, but it is pretty hard to get them both
to work at once.
I was actually quite surprised at how
hard it is to get both of the conditions
to work, so as to get a competitor to
the cosmological constant
interpretation of dark energy.
But at any rate, our reward, if we
succeed, and it happens that the true
vacuum energy is really zero, is that
we would be back where we used to
be, not understanding the vanishing
of the cosmological constant.
I think I’ll conclude by restating the two
admittedly not very original points that I
have aimed to convey:
• Discovery of dark energy greatly changed
how we think about the laws of Nature
• The nature of the change depends
crucially on whether dark energy is a
“cosmological constant”
A last remark is to make an analogy with
General Relativity.
Because the “cosmological constant”
interpretation is so central in our thinking,
tests of it are also central, even though
there is no compelling competing theory.
VIEWS OF DARK ENERGY
Edward Witten
STScI
May 5, 2008