Page 66 - A Brief History of Time - Stephen Hawking

A Brief History of Time - Stephen Hawking... Chapter 8
this cosmological constant would therefore have made the universe expand at an ever-increasing rate. Even in
regions where there were more matter particles than average, the gravitational attraction of the matter would have
been outweighed by the repulsion of the effective cosmological constant. Thus these regions would also expand in
an accelerating inflationary manner. As they expanded and the matter particles got farther apart, one would be left
with an expanding universe that contained hardly any particles and was still in the supercooled state. Any
irregularities in the universe would simply have been smoothed out by the expansion, as the wrinkles in a balloon are
smoothed away when you blow it up. Thus the present smooth and uniform state of the universe could have evolved
from many different non-uniform initial states.

In such a universe, in which the expansion was accelerated by a cosmological constant rather than slowed down by
the gravitational attraction of matter, there would be enough time for light to travel from one region to another in the
early universe. This could provide a solution to the problem, raised earlier, of why different regions in the early
universe have the same properties. Moreover, the rate of expansion of the universe would automatically become
very close to the critical rate determined by the energy density of the universe. This could then explain why the rate
of expansion is still so close to the critical rate, without having to assume that the initial rate of expansion of the
universe was very carefully chosen.

The idea of inflation could also explain why there is so much matter in the universe. There are something like ten
million million million million million million million million million million million million million million (1 with eighty
zeros after it) particles in the region of the universe that we can observe. Where did they all come from? The answer
is that, in quantum theory, particles can be created out of energy in the form of particle/antiparticle pairs. But that just
raises the question of where the energy came from. The answer is that the total energy of the universe is exactly
zero. The matter in the universe is made out of positive energy. However, the matter is all attracting itself by gravity.
Two pieces of matter that are close to each other have less energy than the same two pieces a long way apart,
because you have to expend energy to separate them against the gravitational force that is pulling them together.
Thus, in a sense, the gravitational field has negative energy. In the case of a universe that is approximately uniform
in space, one can show that this negative gravitational energy exactly cancels the positive energy represented by the
matter. So the total energy of the universe is zero.

Now twice zero is also zero. Thus the universe can double the amount of positive matter energy and also double the
negative gravitational energy without violation of the conservation of energy. This does not happen in the normal
expansion of the universe in which the matter energy density goes down as the universe gets bigger. It does happen,
however, in the inflationary expansion because the energy density of the supercooled state remains constant while
the universe expands: when the universe doubles in size, the positive matter energy and the negative gravitational
energy both double, so the total energy remains zero. During the inflationary phase, the universe increases its size
by a very large amount. Thus the total amount of energy available to make particles becomes very large. As Guth
has remarked, “It is said that there’s no such thing as a free lunch. But the universe is the ultimate free lunch.”
The universe is not expanding in an inflationary way today. Thus there has to be some mechanism that would
eliminate the very large effective cosmological constant and so change the rate of expansion from an accelerated
one to one that is slowed down by gravity, as we have today. In the inflationary expansion one might expect that
eventually the symmetry between the forces would be broken, just as super-cooled water always freezes in the end.
The extra energy of the unbroken symmetry state would then be released and would reheat the universe to a
temperature just below the critical temperature for symmetry between the forces. The universe would then go on to
expand and cool just like the hot big bang model, but there would now be an explanation of why the universe was
expanding at exactly the critical rate and why different regions had the same temperature.

In Guth’s original proposal the phase transition was supposed to occur suddenly, rather like the appearance of ice
crystals in very cold water. The idea was that “bubbles” of the new phase of broken symmetry would have formed in
the old phase, like bubbles of steam surrounded by boiling water. The bubbles were supposed to expand and meet
up with each other until the whole universe was in the new phase. The trouble was, as I and several other people
pointed out, that the universe was expanding so fast that even if the bubbles grew at the speed of light, they would
be moving away from each other and so could not join up. The universe would be left in a very non-uniform state,
with some regions still having symmetry between the different forces. Such a model of the universe would not
correspond to what we see.

In October 1981, I went to Moscow for a conference on quantum gravity. After the conference I gave a seminar on
the inflationary model and its problems at the Sternberg Astronomical Institute. Before this, I had got someone else
to give my lectures for me, because most people could not understand my voice. But there was not time to prepare
this seminar, so I gave it myself, with one of my graduate students repeating my words. It worked well, and gave me

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