麻豆传媒

ALBERT EINSTEIN鈥檚 general theory of relativity, the modern description of
gravity, is one of the most successful scientific theories ever. It has
passed, with flying colours, every test that scientists have been able to
dream up. Yet one dramatic prediction of Einstein鈥檚 theory remains
tantalisingly just out of reach 鈥� the detection of gravitational waves. Their
discovery would be the jewel in the crown of relativity theory. But, more than
that, they would tell us about fundamental processes that shaped the Universe
from its earliest days.

Einstein鈥檚 theory explains gravity in terms of curved spacetime. If space-
time can curve it can surely ripple too, and gravitational waves are often
described as ripples in space-time. They travel like waves on a pond,
spreading outwards from sources of extreme gravitational disturbance such as
the collision of a star with a black hole. They cause a temporary distortion
in space-time and then travel onwards, usually leaving no trace at all.
Astrophysicists have been on the trail of gravitational waves for decades. But
no one has found them yet.

Even so, nobody seriously doubts the existence of gravitational waves. For
one thing, they explain changes seen in an unusual object discovered in 1974,
thought to be a binary pulsar, in which two neutron stars (one of them a
pulsar) orbit closely around one another. Each of these stars has roughly the
mass of the Sun packed into a sphere only a few kilometres across 鈥� as dense
as an atomic nucleus. According to Einstein鈥檚 theory, the two orbiting neutron
stars should generate ripples in space-time which carry energy away from the
system. And as they lose energy, the two stars should spiral together at a
particular rate. The observed behaviour of the binary pulsar exactly matches
the prediction.

Relativity theory predicts that the passage of gravity waves should create
minute distortions in the path of a light beam, and this is the basis of some
experiments aimed at detecting them. Some of these projects are big science.
Experiments are under construction in the US and Europe that involve lasers in
vacuum tunnels several kilometres long. Smaller-scale experiments with lasers,
and attempts to spot the effects of passing gravitational waves on large metal
bars, have yet to meet with success.

So some scientists are now considering another way of hunting down gravity
waves. By distorting space-time when the Universe was young, gravitational
waves may have left an imprint on the cosmic microwave background radiation 鈥�
the sea of weak radio noise that fills the entire Universe. And this imprint
may show up in the signal detected by the COBE satellite as it surveyed the
microwave background. Scientists believe that by studying data on the
microwave background they may be able to steal a march on their colleagues who
are still building the laser-interferometer experiments, by winning the race
to find unequivocal proof of the existence of gravitational radiation.

Radiation relic

The cosmic microwave background radiation is the most important
observational tool available to cosmologists. It is equivalent to radiation
from an object with a temperature of 2.7 kelvin that radiates perfectly.
Cosmologists explain it as the relic radiation from the big bang, the fireball
in which the Universe was born. This radiation was originally much hotter, but
has been cooling as the Universe has expanded over the past 15 billion years
or so. Just after the big bang, the Universe was too hot for ordinary atomic
matter to form, and positively charged nuclei and negative electrons remained
separated in a plasma. Electromagnetic radiation, including microwave
radiation, can only interact with particles that are charged, and it
interacts, or 鈥渃ouples鈥�, very effectively with such a plasma. But this
coupling between microwave radiation and plasma occurred for the last time
about 300 000 years after the big bang itself. The entire Universe was then at
the temperature at the surface of the Sun today (about 6000 K) and the last
few remaining free electrons were being captured by atomic nuclei to make
stable atoms. Cosmologists believe that the pattern of background radiation we
now see reflects the distribution of matter in the Universe at this time, when
coupling had ceased.

Irregularities

The temperature of the background radiation is virtually the same from all
parts of the sky, to an accuracy of better than a few thousandths of a kelvin.
This tells us that the Universe was a very smooth and uniform place in the
distant past. By contrast, matter in the Universe today is not spread evenly:
it is clumped together into galaxies, stars and planets. Even galaxies such as
our own Milky Way are gathered together into clusters of galaxies, and those
clusters into superclusters. Something must have happened between the creation
of the microwave background and the present to bring about such a dramatic
change.

Though the Universe was very smooth at the time when the microwave
background stopped interacting with electrons, most cosmologists believe that
it was not perfectly smooth 鈥� some regions were fractionally more dense than
others. The denser regions had more matter than their neighbours, so their
extra gravity pulled matter towards them. In this way the original
irregularities would have been amplified by the force of gravity (See Diagram). Even tiny initial irregularities of
this kind, known a density perturbations, could have grown to form the
structures we see in the Universe today.FIG-mg19504101.GIF

If this is right, evidence of the original irregularities should be
apparent as minute differences in the temperature of the microwave background
when we look in different directions. In effect, radiation from regions of
higher density has to escape a greater gravitational pull on its way to our
part of the Universe, losing energy in the process and becoming cooler than
radiation from neighbouring regions that have lower density. A hot spot in the
microwave background would indicate a region of low density in the young
Universe, while a cool spot would indicate a region of higher than average
density.

An additional complicating factor is the possibility that most of the
matter in the Universe today is in the form of dark matter which can influence
the action of gravity on the conventional visible matter (see 麻豆传媒,
Inside Science, 鈥淒ark matter and the universe鈥� 19 March 1994). Nevertheless,
by working backwards from the present clumpiness of the Universe, most
estimates of the size of the expected temperature irregularities, or
anisotropies, in the background radiation come to around 1 part in 100 000.
And because the microwave background has a temperature of just under 3 K, the
anticipated deviations from point to point are only tens of microkelvins.

The background radiation was discovered in the 1960s. In the 1970s and
1980s, as observations of the radiation became more refined, cosmologists
began to worry that it might be too smooth, and that their theories of how
gravity could make irregularities grow would have to be revised. Then in 1992,
observations made by the COBE satellite revealed the long sought for
irregularities in the background radiation with just about the right size to
have been caused by density perturbations.

But there is an exciting alternative. The anisotropies may be caused at
least in part by gravitational waves. This possibility was first advanced in
the mid-1980s, through work by Roberto Fabbri and Martin Pollock in Italy, by
Larry Abbott and Mark Wise in the US, and by Alexei Starobinsky at the Landau
Institute of Theoretical Physics in Moscow. But at the time, their work was
treated as a curiosity, and remained largely unknown. COBE changed all that.
Within months, a flood of papers appeared 鈥渞eminding鈥� scientists of the
earlier work and reassessing it in the light of present thinking. The
conclusion: what COBE was seeing could be caused by gravitational waves.

The passage of a gravitational wave has a curious effect on space-time, and
therefore on any distribution of matter embedded in it. Suppose a gravity wave
travels out of the page towards your eye. Just as with electromagnetic waves,
the action all happens in the plane perpendicular to the direction in which
the wave travels. Imagine a circle in that plane, drawn on the page. As the
wave passes, the circle experiences a compression from top to bottom, and a
stretching from side to side, turning it into an oval. Then the pattern
reverses, as the oval passes back to the circular form and then becomes
stretched from top to bottom and squeezed from side to side (see Diagram). If gravitational waves were passing
through the Universe just as the microwave background decoupled from matter,
they would have permanently influenced the pattern of the microwave
background. The radiation would have been moved in and out along with the
matter. Where matter and radiation were pulled towards our part of the ancient
Universe, their velocity and energy would have increased, and therefore the
temperature of the microwaves would have increased. Where gravitational wave
motions pushed matter away from our part of the ancient Universe, their
temperature would have been reduced. Because the cooling of the microwave
radiation has continued uniformly with the expansion of the Universe, these
differences in the microwave background will have been preserved.FIG-mg19504102.GIF

Like any wave, the longer the gravitational wave鈥檚 wavelength, the more
slowly it oscillates. For gravitational waves long enough for their effect to
be seen today, their oscillation would have been slow enough 300 000 years ago
that the decoupling of the microwave radiation would have happened much more
quickly than the changes due to the passage of the waves. So the gravitational
waves would have been caught, as in a snapshot, with the microwaves recording
their positions in the wave motion at that time. Although the gravitational
waves continued, their mark, a pattern of hot and cold spots in the microwave
background, would be left like a fossilised imprint on the radiation. It is
these marks that COBE might have seen. Further gravity waves can have had no
influence, because the radiation became decoupled and no longer interacted
with matter in this way.

Quantum uncertainties

To have left marks on the microwave background large enough for us to be
able to observe today, the gravitational waves would have had to be a sizable
fraction 鈥� at least a few per cent 鈥� of the size that our entire Universe was
at that time. Shorter-wavelength ripples would produce variations on too small
a scale. Nowadays, what seem to us to be exceptionally violent events such as
the collision of two black holes or material falling into a neutron star are
believed to generate only relatively short-wavelength gravitational waves.
Long-wavelength ripples in the early Universe would have required something
even more drastic than this. Luckily, a theoretical model of the very early
Universe predicts the existence of the required long-wavelength gravitational
radiation.

This model is known as the inflationary Universe, a popular extension of
the standard big bang model in which, during its very early stages, the
Universe experiences an epoch of extremely rapid growth. The model says that
the Universe can generate both density perturbations and gravitational waves.
This happens by means of an extraordinary mechanism that combines notions of
gravitation and quantum mechanics.

One of the main features of the quantum world is uncertainty. A rule of
quantum mechanics, called the Heisenberg uncertainty principle, says that
absolutely everything is subject to uncertainties. These take the form of tiny
variations of all kinds, called quantum fluctuations, which take place on a
scale much smaller than that of an atom. For instance, subatomic particles can
pop into and out of existence in a tiny fraction of a second, and space-time
itself ripples like the surface of the sea in a storm over distances measured
in terms of the Planck length, a mere 10^鈭�33 of a centimetre.
The extremely rapid expansion associated with inflation can take these quantum
fluctuations and stretch them to such enormous sizes that they become the
irregularities we see as the structure of the Universe today.

Swing time

To understand how this might happen, think of a pendulum 鈥� the physicist鈥檚
ideal with a massless string 鈥� swinging backwards and forwards. As it swings,
suppose we allow the length of the string to increase dramatically, so that
its length doubles with each passing second. As the rate at which a pendulum
swings is proportional to its length, the rate of swing slows down as the
string extends. What eventually happens is rather surprising. As the string
continues to lengthen and the rate of swing becomes ever slower, the pendulum
is unable to finish its final swing and finishes up trapped at an angle from
the vertical.

The same thing happens with quantum fluctuations caught up in the expansion
of the inflationary Universe and stretched to vast sizes. As this happens,
their rate of fluctuation slows dramatically until, like the pendulum, they
find themselves trapped in a state displaced away from that of the lowest
energy. And since neither matter in the Universe, nor the gravitational force
itself, can avoid uncertainties, two things result. The stretched fluctuations
in the matter of the Universe become irregularities in the density, which
later grow under the influence of gravity to form galaxies and galaxy
clusters. Those in the gravitational field become gravitational waves.

In fact, physicists are still working out precisely how to combine
gravitation and quantum mechanics into a single, fully consistent picture (see
鈥淐an gravity take a quantum leap?鈥�, 麻豆传媒, 10 September). This raises
a potential problem when trying to describe in mathematical terms how
inflationary expansion leads to density perturbations and gravitational waves:
working out the gravitational forces caused by the quantum fluctuations
themselves is impossibly complicated. Fortunately, as explained earlier, the
early Universe is observed to be very smooth, which implies that the initial
irregularities must be small, and the quantum gravitational forces can be
ignored. Starobinsky pioneered such calculations of the size of the
gravitational waves 15 years ago, and they have since been refined and
extended by other researchers to cover density perturbations. Surprisingly,
the calculations turn out to be quite simple and unambiguous, and their
results are widely accepted by cosmologists.

Unfortunately, there are several possible models of inflation, and each
gives a different prediction of the effect of gravity waves on the microwave
background. So although the uncertainty principle tells us that there must be
both density perturbations and gravitational waves, we do not know the
relative importance of their contributions to the background radiation. So how
will we know whether what we are seeing is due to gravity waves?

It turns out that the way to distinguish between the two contributions is
to look at differences in the pattern of the anisotropies at different
resolutions. Calculations show that if gravitational waves are responsible,
then there should be very little fine detail in anisotropy maps such as the
COBE plots (see Diagram). This is because, as
gravitational waves oscillate, the expansion of the Universe decreases their
amplitude. Remember that the longer the wavelength is, the smaller the
oscillation. It turns out that waves that are long enough to show up at large
scales (above about 1掳) on the microwave background did not have time to
oscillate even once by the time the microwave background decoupled, so that
expansion of the Universe did not affect their amplitude. Shorter waves had
time to oscillate, and the shorter they were, the more oscillations, and the
greater the loss of amplitude. So at scales of less than 1掳, the effect of
the gravitational waves begins to fall off sharply. Irregularities in density,
on the other hand, become larger under the influence of gravity, and should
produce lots of fine detail in the maps.FIG-mg19504103.GIF

Angling for waves

Sadly, the COBE satellite does not have sharp enough sight to make this
distinction. It takes in a beam with a spread of 7掳 which gives it an
excellent overall view, but fine details are hopelessly blurred. Some of the
structure in the background radiation seen by COBE may be due to gravitational
waves, but the observations are not good enough to prove this. However, the
success of COBE has encouraged many more experiments designed to detect the
anisotropies across a wide range of angular scales (see 鈥淯p, up and away to
the beginning of time鈥�, 麻豆传媒, 22 October). Separate experiments in
the US, Italy and Britain are all announcing detections of temperature
irregularities. Many of these experiments are carried out at a resolution of
around 1掳, a scale at which the influence of gravitational waves should
have waned dramatically. So differences between their observations and those
of COBE may allow physicists to untangle the anisotropies into the two
separate components, and reveal if COBE鈥檚 observations have been affected by
gravitational waves.

Such an approach was pioneered last year by a team led by Robert
Crittenden, then at the University of Pennsylvania. The researchers surveyed
observations from several studies at different angular scales for the telltale
sign 鈥� the deviations in temperature at degree-scale resolution being smaller
than expected. Their preliminary results suggest that gravitational waves are
present, but they could not make a convincing case that the pattern was
unlikely to have arisen simply by chance. Moreover, researchers at the
University of California at Berkeley have since pointed out that uncertainties
in our understanding of key aspects of the Universe鈥檚 evolution, such as the
expansion rate, make it even more difficult to be sure that the effect seen by
Crittenden was caused by gravity waves.

Even taking the uncertainties about the Universe鈥檚 evolution into account,
Crittenden and colleagues now believe they will be able to identify the effect
of gravitational waves only if they cause more than 10 per cent of the total
anisotropy signal; researchers at Fermilab near Chicago say that a figure of
at least 20 per cent is required. If the true inflation model is one that
produces few gravitational waves, the disappointed researchers will not be
able to prove the existence of the waves 鈥� they will have to be content with
ruling out those models that predict large amounts of gravitational waves. But
if inflation has provided enough waves, then their detection in the microwave
background will only be a matter of time. Either way, the pressure will then
be on the traditional gravity wave hunters to detect the waves from the stars
and black holes of our own back yard.