Three Roads To Quantum Gravity

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THREE ROADS TO QUANTUM GRAVITY
the evolution of our universe. This cosmological constant
would make the energy density of empty space equal to
about twice the current value of the energy density of everything
else that has been observed. This may seem surprising,
but the point is that the energy density of all the kinds of
matter that have been observed is currently very small. This
is because the universe is very old. When measured in fundamental
units, its present age is about 10 60 Planck times.
And it has been expanding all this time, thus diluting the
density of matter.
The energy density due to the cosmological constant does
not, as far as we know, dilute as the universe expands. This
gives rise to a very troubling question: Why is it that we live
at a time when the matter density has diluted to the point
that it is of the same order of magnitude as the density due
to the cosmological constant?
I do not know the answer to any of these questions. Neither,
I think, does anyone else, although there are a few interesting
ideas on the table.
However, the apparent fact that the cosmological constant
is not zero has big implications for the quantum theory of
gravity. One reason is that it seems to be incompatible with
string theory. It turns out that a mathematical structure that
is required for string theory to be consistent—which goes by
the name supersymmetry—only permits the cosmological
constant to exist if it has the opposite sign from the one that
has apparently been observed. There are some interesting
studies of string theory in the presence of a negative cosmological
constant, but no one so far knows how to write down
a consistent string theory when the cosmological constant is
positive—as has apparently been observed.
I do not know if this obstacle will kill string theory—string
theorists are very resourceful, and they have often expanded
the definition of string theory to include cases once thought
impossible. But string theorists are worried, for if string theory
cannot be made compatible with a positive cosmological
constant—and that continues to be what the astronomers observe—then
the theory is dead.