Eternally accelerating universe without event horizon

Increasing astronomical evidence indicates that the expansion of the universe is accelerating. By simply solving Einstein equations we show in this Letter that a wide class of generic quintessence models leading to eternal acceleration is associated with spacetime static metrics which do not exhibit future event horizons, and therefore do not pose the same problems for string theory as asymptotic de Sitter spaces. (C) 2001 Elsevier Science B.V. All rights reserved.