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BIG BANG
Einstein's
elusive ripples
Feature, 5 November 1994, page one
Years of scouring the Universe for
Einstein's gravitational waves have
proved fruitless. But now, say
Andrew Liddle and John Gribbin,
cosmologists think they may have
found telltale signs in the microwave
background radiation
Albert Einstein's 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's
theory remains tantalisingly just out of reach -
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's theory explains gravity in terms of
curved space-time. 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 - as dense as an atomic nucleus.
According to Einstein's 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 - 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
'couples', 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.
Feature, 5 November 1994, page two
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 - 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 (Figure 1).
Even tiny initial irregularities of this kind,
known as density perturbations, could have
grown to form the structures we see in the
Universe today.
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 New
Scientist, Inside Science, 'Dark matter and the
universe' 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 'reminding' 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.
Feature, 5 November 1994, page three
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 (Figure
2). 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.
Like any wave, the longer the gravitational
wave's 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 - at least a
few per cent - 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 10-33 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 - the physicist's ideal with a
massless string - 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.
Feature, 5 November 1994, page four
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 'Can gravity take a quantum leap?', New
Scientist, 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 (Figure 3). 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 degree)
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 degree, 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.
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 degree 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 'Up,
up and away to the beginning of time', New
Scientist, 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 degree, 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's observations have been
affected by gravitational waves.
Feature, 5 November 1994, page five
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 -
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's 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's 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 - 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.