Summary: Nuclear Physics B195 (1982) 76-96
~' North-Holland Publishing Company
STABILITY OF GRAVITY WITH A COSMOLOGICAL CONSTANT
L.F. ABBOTT and S. DESER ~
CERN, Geneva, Switzerland
Received 26 August 1981
The stability properties of Einstein theory with a cosmological constant A are investigated.
For A > 0, stability is established for small fluctuations, about the de Sitter background, occurring
inside the event horizon and semiclassical stability is anal~ed. For A < 0, stability is demonstrated
for all asymptotically anti-de Sitter metrics. The analysis is based on the general construction of
conserved flux-integral expressions associated with the symmetries of a chosen background. The
effects of an event horizon, which lead to Hawking radiation, are expressed for general field
hamiltonians. Stability for A < 0 is proved, using supergravity techniques, in terms of the graded
anti-de Sitter algebra with spinorial charges also expressed as flux integrals.
The vacuum energy density of the universe is known to be of magnitude less than
(0.003 eV)4. To achieve such a small energy density in the standard models of strong,
weak and electromagnetic interactions requires extraordinary and unnatural fine
tuning of parameters. This fine tuning problem leads us to wonder why the
cosmological constant (defined as 87rG times the vacuum energy density) is so small.