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A generalisation of the asymptotic wormhole boundary condition for the caseof spacetimes with a cosmological horizon is proposed. In particular, weconsider de Sitter spacetime with small cosmological constant. The wavefunctions selected by this proposal are exponentially damped in WKBapproximation when the scale factor is large but still much smaller than thehorizon size. In addition, they only include outgoing gravitational modes inthe region beyond the horizon. We argue that these wave functions representquantum wormholes and compute the local effective interactions induced by themin low-energy field theory. These effective interactions differ from those forflat spacetime in terms that explicitly depend on the cosmological constant.Comment: 10 pages, LaTeX 2.O9, no figure

WORMHOLES IN SPACETIMES WITH COSMOLOGICAL HORIZONS