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Summary: EXISTENCE AND STABILITY OF EVEN DIMENSIONAL
ASYMPTOTICALLY DE SITTER SPACES
MICHAEL T. ANDERSON
Abstract. A new proof of Friedrich's theorem on the existence and stability of asymptotically
de Sitter spaces in 3+1 dimensions is given, which extends to all even dimensions. In addition we
characterize the possible limits of spaces which are globally asymptotically de Sitter, to the past
and future.
1. Introduction.
Consider globally hyperbolic vacuum solutions (M n+1 ; g) to the Einstein equations with cosmo-
logical constant > 0, so that
(1.1) Ric g
R g
2 g + g = 0:
The simplest solution is (pure) de Sitter space on M n+1 = R S n , with metric
(1.2) g dS = dt 2 + cosh 2 (t)g S n (1) :
More generally, let (N n ; g N ) be any compact Riemannian manifold with metric g N satisfying the
Einstein equation Ric g N
= (n 1)g N . Then the (generalized) de Sitter metric
(1.3) g N
dS = dt 2 + cosh 2 (t)g N ;
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