There are now two cosmological constant problems. The old cosmological
constant
problem is to understand in a natural way why the vacuum energy density
_{V}
is not very much larger. We can reliably calculate some contributions to
_{V}, like
the energy density in fluctuations in the
gravitational field at graviton energies nearly up to the Planck scale,
which is
larger than is observationally allowed by some 120 orders of magnitude. Such
terms in _{V}
can be cancelled by other contributions that we can't
calculate, but the cancellation then has to be accurate to 120 decimal places.
The new cosmological constant problem is to understand why
_{V} is not only
small, but also, as current Type Ia supernova observations seem to
indicate,
^{(2)}
of the same order of magnitude as the present mass density of the universe.

The efforts to understand these problems can be grouped into four general
classes. The first approach is to imagine some scalar field coupled to
gravity in such a way that
_{V} is
automatically cancelled or nearly cancelled when the scalar
field reaches its equilibrium value. In a review article over a decade
ago ^{(3)}
I gave a sort of
`no go' theorem, showing why such attempts would not work without the
need for a
fine tuning of parameters that is just as mysterious as the problem we started
with. I wouldn't claim that this is conclusive -
other no-go theorems have been evaded in the past - but so far no one has
found a way out of this one. The second approach is to imagine some sort of
deep symmetry, one that is not apparent in the effective field theory that
governs phenomena at accessible energies, but that nevertheless constrains the
parameters of this effective theory so that
_{V} is zero
or very small. I
leave this to be covered in the talk by Edward Witten. In this talk I will
concentrate on the third and fourth of these approaches, based respectively on
the idea of quintessence and on versions of the anthropic principle.

^{2} A. G. Riess et al.:
Astron. J. **116**, 1009 (1998);

P. M. Garnavich et al.: Astrophys. J. **509**, 74 (1998);

S. Perlmutter et al.: Astrophys. J. **517**, 565 (1999).
Back.

^{3} S. Weinberg:
Rev. Mod. Phys. **61**, 1 (1989).
Back.