The expanding Universe

These days, many non-scientists will have come across the concept
of the expanding Universe. But what does it mean? Is it just
another strange idea devised by scientists based on a scrap or two
of evidence that could just as well have been interpreted in another way? The answer is no. There is now so much evidence in support
of the observation that our Universe is getting bigger that we can
no longer be in any serious doubt. The expansion was confirmed
as long ago as 1929 when the American astronomer Edwin Hubble
made a remarkable discovery, but only after several cosmologists
had already predicted the effect theoretically.
The first modern day cosmologist was, of course, Einstein
himself. Soon after he completed his general theory of relativity in
1915 he began using his equations to describe the global properties
of the whole Universe. He soon came across a serious problem.
If, at a given time, all the galaxies in the Universe are stationary
relative to each other, and provided the Universe was finite in
size, then their mutual gravitational attraction will cause them to
begin to converge on each other and the Universe would collapse
in on itself. It could not remain static. This is actually quite a
tricky concept to come to grips with (and not the only one we
will encounter in this chapter). This is because, na¨ıvely, you
would think that the Universe as defined by its volume of space
should remain the same size while the matter it contains gravitates
towards its ‘centre’. This is quite wrong. For one thing we will see
that the Universe does not have a centre at all and, in any case, we
have learnt that gravity affects space itself and does not simply act
on the matter ‘within’ it.
The prediction of his own equations bothered Einstein. The
widely held view at the time, and Einstein was no exception to this
despite his many other revolutionary ideas, was that the Universe,
at the level of galaxies and larger, should be static and unchanging.
Whether it had been thus for ever or whether a divine creator
had conjured it into existence at some time in the distant past
did not matter. Both views supported a picture of the present
Universe that was constant. The idea of an evolving universe
was both alien and unnecessary. So, when Einstein’s equations
of general relativity seemed to indicate that the Universe should
be shrinking he decided to patch things up. He argued that, in
order to balance the inward pull of gravity there needed to be an
opposing force of antigravity, known as the cosmic repulsion force,
which would balance the gravitational attraction and keep all the galaxies apart and the Universe stable. The difference between
gravity and antigravity is the same as the difference between the
attractive force that pulls the north pole of one magnet towards
the south pole of another and the repulsive force that pushes two
north poles apart. This cosmic repulsion force appeared in the
mathematics as a number, which Einstein called the cosmological
constant. It was denoted in his equations by the Greek letter
lambda. (In advanced mathematics it is not enough to use x, y
and z for the unknown quantities. We soon run out of letters
in the alphabet and start raiding Greek letters—with pi being
the best-known example of this). What Einstein had suggested
was a mathematical trick in order to achieve his model of a static
universe.
A few years after Einstein’s initial work, the Soviet
cosmologist Aleksandr Friedmann published a paper in which he
suggested doing away with the cosmic repulsion (by setting the
value of the cosmological constant to be equal to zero in Einstein’s
equations). Friedmann found that when he applied Einstein’s
equations of general relativity to the Universe and worked through
the maths, he always found solutions (other equations) which
predicted that the distance between any two points in space was
stretching over time. He had found theoretically that the Universe
was getting bigger all the time. Two other scientists came to the
same conclusions round about the same time. They were the
Dutch astronomer Willem de Sitter and the Belgian cosmologist
(and priest) Georges Lemaˆıtre.
This may seem rather surprising if we think what the action of
gravity would be when there is no cosmic repulsion force to hold
the matter in the Universe apart. Surely, without a cosmological
force of repulsion the Universe should be shrinking not growing.
But an expanding universe can be understood in the following
way. Imagine that something had set the Universe expanding in
the first place, an initial explosion. The gravitational pull of all the
matter in the Universe would then be trying to slow the expansion
rate down. This was the essence of Friedmann’s argument. If there
is no cosmic force of repulsion to balance the attraction of gravity,
and the Universe had started off expanding, then it would have to be either expanding or contracting at the moment. It could not
remain poised between expansion and collapse since that would
be unstable.
Asimple example to demonstrate this would be what happens
to a ball on the side of a smooth slope. If placed half way up
the slope it will always roll down. But if we did not see how
the ball came to be on the slope in the first place then we would
expect it to be either rolling up the slope (corresponding to an
expanding universe) or down the slope (a collapsing universe),
never standing still. Of course the only way it could be rolling
up the slope would be if it had been deliberately given an initial
push, but in that case it would immediately begin to slow down
and eventually start rolling down again. Now imagine that the
slope levels off at the top. Provided the ball was initially set rolling
up the slope fast enough it could make it to the top. Once there,
it could then continue to roll along indefinitely without slowing
down (of course I am ignoring friction and wind resistance here
since a real ball would eventually stop even on a flat surface).
Assuming that the ball was always given the same initial
speed up the slope, what governs its ultimate fate will then be
how high the top is. If it is too high, the ball will not be able to
reach the top and will roll down again.
This is how we can view the expansion of the Universe. The
effectiveness of the gravitational pull depends on the amount
of matter the Universe contains. By matter I do not just mean
all the stars, planets and other solid objects, but everything of
substance in the Universe. This may be in the form of dust, gas,
subatomic particles, even pure energy. So, whether the Universe
is now contracting or expanding depends on how much matter it
contained and how long the gravitational pull of all this matter
had been applying the brakes on its initial expansion. This was
the essence of Friedmann’s model universe.
No one, not even Einstein, was prepared to believe
Friedmann’s results, not until experimental proof was found. This
came just a few years later. Unfortunately, Friedmann died in 1925
and did not live to see it.