STATISTICAL ENTROPY OF DE SITTER SPACE

Quantum gravity in 2+1 dimensions with a positive cosmological constan t can be represented as an SL(2,C) Chern-Simons gauge theory. The symm etric vacuum of this theory is a degenerate configuration for which th e gauge fields and spacetime metric vanish, while de Sitter space corr esponds to a highly excited thermal state. Carlip's approach to black hole entropy can be adapted in this context to determine the statistic al entropy of de Sitter space. We find that it equals one-quarter the area of the de Sitter horizon, in agreement with the semiclassical for mula.