Three Roads To Quantum Gravity

POSTSCRIPT 221
But there is a second reason why a positive cosmological
constant is troubling for quantum theories of gravity, including
string theory. As the universe continues to expand, the
energy density due to matter will continue to dilute. But the
cosmological constant is believed to remain stable. This
means that there will be a time in the future when the cosmological
constant comprises most of the energy density in
the universe. After this the expansion will accelerate—indeed
the effect is very similar to the inflation proposed for
the very early universe.
To be an observer in an inflating universe is to be in a very
poor situation. As the universe inflates, we will see less and
less of it. Light cannot keep up with the acceleration of the
expansion, and light from distant galaxies will no longer be
able to reach us. It would be as if large regions of the universe
had fallen behind the horizon of a black hole. One by
one distant galaxies will go over a horizon, to a zone from
which their light will never again reach us. With the value
apparently measured, it is only a matter of a few tens of billions
of years before observers in a galaxy see nothing
around them except their own galaxy surrounded by a void.
In such a universe, the considerations of Chapters 1–3 become
crucial. A single observer can only see a small portion
of the universe, and that small portion will only decrease
over time. No matter how long we wait, we will never see
more of the universe than we do now.
Tom Banks has expressed this principle beautifully. There
is a finite limit to the amount of information that any observer
in an inflating universe may ever see. The limit is that
each observer can see no more than G 3π
2 L bits of information,
where G is Newton’s constant and L is the cosmological constant.
Raphael Bousso called this the N-bound and argued
that this principle may be derived by an argument that is
closely related to Bekenstein’s bound, which is described in
Chapters 8 and 12. The principle seems to be required by the
second law of thermodynamics.
As the universe expands, we would expect that it contains
more and more information. But, according to this principle,