麻豆传媒

LAST year the world of astronomy was shaken to its core by the discovery that
supernovae across the Universe were fainter and therefore further away than
their red shift suggested they had any right to be. Somehow space has stretched
out more than it should have done since the light from those exploding stars set
off across the Universe all those billions of years ago. Contrary to all
expectations, the Universe鈥檚 expansion is speeding up (see 鈥淭o infinity and
beyond,鈥� 11 April 1998, p 26).

It鈥檚 not surprising astronomers were shocked. They thought that the only
force acting on the cosmic scale was gravity and that gravity was pulling the
galaxies together, braking the Universe鈥檚 expansion. If the expansion is
speeding up, they realised, something must be opposing gravity, pushing instead
of pulling. The only candidate they could come up with to do this is empty
space. But how can it push galaxies apart? How can empty space be 鈥渟pringy鈥�?

Dominant force

It turns out that space can be springy if it is made from an entirely new
material鈥攓uite different from the matter and radiation we are used to. We
can鈥檛 see this material but we know it must be packed with energy. The problem
is that theorists are struggling to understand the behaviour of this exotic
material, predicting that it ought to have far more energy than it does. What鈥檚
more, they can鈥檛 explain why the springiness has become the dominant force at
this particular point in the history of the Universe. Hot on the heels of the
supernova results, however, some intriguing new ideas are beginning to
emerge.

Einstein鈥檚 theory of gravity tells us how gravity can be repulsive鈥攖hat
is, push as well as pull. To understand how, you first need to know that in the
equations of general relativity, gravity is generated by two things: the energy
density of a material and its pressure. Strictly speaking, pressure is a form of
energy鈥攖he energy of gas particles drumming on the walls of a container,
for instance. However, Einstein deliberately didn鈥檛 lump pressure together with
energy density in his equations. That鈥檚 because he had a hunch the Universe
could also contain a material with 鈥渋ntrinsic pressure鈥�. This material is the
key to understanding how gravity can push instead of pull.

In Einstein鈥檚 equations, if you add the energy density term to the pressure
term and get a positive result, gravity pulls. If the sum is negative, gravity
pushes. It鈥檚 as simple as that. But how can the sum of the terms be negative?
Well, for all the usual stuff in today鈥檚 Universe鈥攎atter and light
radiation鈥攖he sum is always positive, since their energy densities are
positive and their pressures negligibly small.

But what if the Universe contains an exotic material with a large intrinsic
negative pressure? One that would be big enough to influence gravity?

Inward tension

Negative pressure is not such a bizarre idea as it first seems. It is simply
a force pulling inwards like the tension in a piece of stretched elastic. This
means that space can be springy providing it is made of a weird material with a
huge inward tension. This is a very counterintuitive idea. After all, how can a
material that pulls inwards drive galaxies away from each other? The key is to
understand that the negative pressure of space has no direct effect on its
surroundings. This is because forces are a consequence of pressure differences.
But in space every region is surrounded by other regions, all at exactly the
same pressure. There are no pressure differences. The negative pressure works in
one way only: by generating repulsive gravity through general relativity.

So to explain the way space seems to be stretching, we need to assume that it
has a huge negative pressure. Add in one extra tweak (see 鈥淭he bizarre world of
springy 蝉辫补肠别鈥�) and cosmologists have their exotic material, which they
dub the 鈥淟ambda force鈥�.

One of the advantages of springy space is that it solves a major cosmological
puzzle. Cosmologists like to talk about the density of the Universe in terms of
the so-called 鈥渃ritical density鈥�. This corresponds to a Universe whose total
energy鈥攌inetic plus potential鈥攊s zero. The popular theory of
inflation, which states that the Universe suddenly ballooned in size during the
first split second after its birth, predicts that the Universe should have
precisely the critical density.

A universe that starts off with a density even marginally different from the
critical density will either rocket up in density or plummet down. This fate is
avoided only by a Universe which starts out at precisely critical density. It
hovers there forever.

So, the theory goes, our Universe should either be hovering precisely at the
critical density, or should have a density that鈥檚 dramatically different.
However, if you add together all the matter in the Universe鈥攕tars,
galaxies and invisible 鈥渄ark matter鈥濃�攜ou get an answer that鈥檚 about 30 per
cent of the critical density. That鈥檚 close enough that cosmologists assume that
we are indeed hovering at the critical density, and have simply overlooked the
missing part. Springy space could well fit the bill. The Universe can hover at
the critical density if 30 per cent of its mass is in the form of matter and 70
per cent in the form of springy space, which has mass because of the energy it
contains.

This is great news for astronomers but disastrous news for physicists. Their
theory for the vacuum of space fails completely when it comes to predicting its
energy density. Quantum theory views the particles of nature as excitations of
鈥渇ields鈥� which extend throughout space. For instance, photons are localised
bumps in the electromagnetic field, electrons and positrons are bumps in the
electron-positron field, and so on.

These fields are like guitar strings. Each can vibrate in an infinite number
of modes鈥攆undamental, first overtone, and so on. However, unlike guitar
strings, none of these modes can be damped to zero amplitude. It turns out that
quantum theory sets a minimum energy for every vibration mode. This 鈥渮ero-point
energy鈥� is tiny but when you add up an infinite number of tiny bits of energy,
corresponding to the infinity of vibration modes of all the fields, the answer
you get is infinity. Since the lowest possible energy of the fields corresponds
to the vacuum, quantum theory predicts that the vacuum has an infinite energy
density. Clearly this cannot be right, as otherwise the Universe would long
since have collapsed into a black hole. 鈥淚t鈥檚 a horrible embarrassment,鈥� says
theorist Paul Steinhardt of Princeton University.

Another problem with the quantum picture is that, although the laws of
physics dictate that the vacuum has the same energy density no matter what you
do to it鈥攅xactly the requirement for springy space鈥攖hose same laws
fail to explain how a bunch of zero-point field vibrations can add up to an
exotic material with a negative pressure.

鈥淣obody really understands the connection between the vacuum of quantum
theory and general relativity,鈥� admits Max Tegmark from the Institute of
Advanced Studies in Princeton. 鈥淎ll you can really say is that the vacuum is
weird and the vacuum sucks.鈥�

Actually, you can鈥檛 have an infinite energy density: the laws of physics
break down way at the so-called Planck energy density where gravity challenges
the other forces of nature. So it seems reasonable to suppose that something
stops the vacuum energy going above this. But even then, the energy would be
much too large: the Planck energy density is 10¹²³ times bigger than the
measured energy density of springy space. This has been described by Nobel
laureate Steven Weinberg as 鈥渢he worst failure of an order-of-magnitude estimate
in the history of science鈥�.

While some theorists are wrestling to explain the observed values of the
energy packed into the vacuum, others have a different but related puzzle in
mind: why is the energy density of space today so close to the energy density of
matter? Remember that matter is supposed to make up around 30 per cent of the
energy density of the Universe, with springy space and its dark energy making up
the remaining 70 per cent. The question is, why is the ratio of these numbers so
close to 1?

This is extremely peculiar. Remember that the energy density of space never
changes, no matter how much space stretches (see 鈥淭he bizarre world of springy
蝉辫补肠别鈥�). So the energy density of space is exactly the same today as it was in
the first split-second of the Universe. Contrast this with the energy of matter
and radiation, which have been grossly diluted by the expanding Universe. In
fact, just after the big bang, the energy density of matter and radiation was
10¹⁰⁰ times bigger than that of space. Doesn鈥檛 it seem odd that we have come on
the scene at almost exactly the moment when this ratio has descended from 10¹⁰⁰
to roughly 1?

Of course, it could be a coincidence, but theorists traditionally hate
presuming that there is anything special or unusual about the time we happen to
live in. Steinhardt has a way out of this dilemma. This involves inventing an
entirely new exotic material which he and his colleagues call 鈥渜uintessence鈥�.
鈥淲e鈥檝e stolen the word from the ancient Greeks who thought the elemental
constituents of the world were earth, fire, water and air,鈥� says Steinhardt.
鈥淭hey also speculated about another, purer component鈥攁 fifth essence.鈥�

Like the Lambda force, quintessence is a form of vacuum energy. It exists
throughout space as a so-called 鈥渟calar field鈥�. Fields usually have both
magnitude and direction at every point in space鈥攖he electromagnetic field
is one example. However, a scalar field simply has magnitude. Such a field is
possible in physics. 鈥淪imilar fields drove the dramatic expansion of the
Universe during inflation, although they were much more energetic,鈥� says
Steinhardt. 鈥淭he kind of low-energy field we have in mind might conceivably
arise in superstring theory, which views the fundamental particles of nature as
vibrations of tiny strings.鈥�

So how can quintessence explain the peculiar ratio of the energy densities of
matter and dark energy? Crucially, unlike the Lambda energy, quintessence is not
obliged to stay doggedly constant. 鈥淣ot only can it vary in time and space but
the relationship between its negative pressure and its energy density can vary
in time as well,鈥� says Steinhardt.

That鈥檚 how it solves the ratio problem. Quintessence has an overwhelming
advantage as a component of the vacuum. Because it changes with time,
quintessence might just explain why space鈥檚 energy density is so close to the
energy density of matter when it started off 10¹⁰⁰ times smaller. Crucially it
may interact with matter, allowing it to track the energy density of matter and
zero in on its value. Steinhardt calls it a 鈥渢racker field鈥�. 鈥淲hatever energy
density it starts off at, it homes in on the energy density of matter,鈥� he
says.

So is the dark energy in the form of an unchanging Lambda or quintessence?
Distinguishing between the two alternatives will be hard. The Lambda force grows
remorselessly with the size of the Universe, so it will eventually completely
dominate the gravitational pull from ordinary matter and radiation. It will make
the Universe expand forever and dilute ordinary matter until its density
approaches zero. By contrast, the effect of quintessence will be different:
since it homes in on the energy density of matter, the two will drop away in
step. Nevertheless, it will also lead in the end to an infinitely spread out,
infinitely diluted Universe.

Some physicists think it is premature even to be thinking about
distinguishing between quintessence and the Lambda force. 鈥淚 think the
community鈥檚 gone overboard,鈥� says Rocky Kolb of the Fermi National Accelerator
Laboratory near Chicago. 鈥淚t is so important that we should not rush to judgment
based upon only one direct observation. The Universe has tricked us before.鈥�

Missing quasars

Kolb points out that if the expansion of the Universe is speeding up, it
should increase the volume of space between us and super-bright galaxies known
as quasars, and hence the number of galaxies between us and the quasars. The
more such galaxies, the greater the chance that some of them will be magnifying,
or 鈥渓ensing鈥�, the light of a quasar. 鈥淗owever, there appear to be fewer
gravitationally lensed quasars than would be expected for a Universe with a
Lambda force,鈥� says Kolb.

Although Kolb is sceptical about the supernova results, Tegmark says that
several other pieces of evidence also point in the same direction. For instance,
the Universe is almost the same age as its oldest stars, leaving little time
after the big bang for galaxies and stars to form. 鈥淚f galaxies today are being
driven apart by the Lambda force, then we have overestimated their speed of
recession and so underestimated the time since they were together in the big
bang,鈥� says Tegmark.

Another piece of evidence pointing in the same direction stems from the
cosmic background radiation, the microwave 鈥渁fterglow鈥� of the big bang. It
varies very subtly in temperature across the sky. What everyone is interested in
is the angular scales where the temperature variations are strong. Large-scale
motion of matter and radiation in the early Universe created these variations.
The Lambda force would have changed the scales at which the temperature
fluctuations are strongest. 鈥淎 number of experiments have shown the first peak
appears to be at around 1 degree, which is compatible with a Lambda force,鈥� says
Tegmark.

Better observations are desperately needed to pin the theories down.
Fortunately, we may not have to wait too long. NASA is planning to launch the
Microwave Anisotropy Probe (MAP) and the European Space Agency has a more
extensive mission called Planck in the wings. And astronomers are presently
awaiting the results of several ground-based and balloon experiments that could
tell us more about the Universe鈥檚 dark energy. 鈥淚t鈥檚 extremely exciting,鈥� says
Tegmark.

Springy space must behave in a certain way if it鈥檚 to explain what we see in
the Universe. Even though it is packed with energy, it mustn鈥檛 hinder the motion
of anything travelling through it. That鈥檚 specifically forbidden by Einstein鈥檚
theory of special relativity. The only material that can fill all of space and
not impede the motion of any body travelling through it turns out to have a
pressure equal to minus its energy density: p=鈭抲. It is worth pausing to
consider what this means since it gives space some very bizarre properties.

Negative pressure is like the tension in a piece of elastic: you have to work
to stretch it. In the case of elastic, the work goes into heating the elastic.
If you stretch space, the work you do ends up in the space. So, although you are
diluting the energy density of space by increasing its volume, you are also
adding energy to it. Now here鈥檚 the amazing thing. If p=鈭抲, the amount of
energy you add exactly compensates for the dilution, so the energy density of
space stays constant. It鈥檚 like holding a stack of bank notes between your hands
and finding that as you pull them apart more bank notes appear so the density of
the notes always stays constant.

Because the energy density of space stays constant as space stretches, two
galaxies that are twice as far apart as two others have twice as much springy
stuff between them, so the repulsive force between them is twice as big, and so
on. Since the force grows with distance it can be negligibly small on the
planetary scale yet huge on the cosmic scale, explaining why we noticed it only
when we were able to see things at huge cosmic distances.

Such a cosmic repulsive force was anticipated by Einstein in 1917. When he
applied general relativity to the Universe, he found that it should be either
expanding or contracting. But Einstein favoured a static Universe. So he
suggested the existence of a cosmic repulsive force which perfectly balanced the
force of gravity trying to shrink the Universe. In his equations describing the
Universe, the force appears as a 鈥渃osmological constant鈥�, more commonly known as
鈥淟补尘产诲补鈥�.

In 1929, when Edwin Hubble discovered the Universe was expanding, Einstein
abandoned the Lambda force, famously calling it his 鈥渂iggest blunder鈥�.