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There are now two cosmological constant problems. The old cosmological constant problem is to understand in a natural way why the vacuum energy density rhoV is not very much larger. We can reliably calculate some contributions to rhoV, 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 rhoV 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 rhoV 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 rhoV 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 rhoV 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.

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