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We investigate the instanton solution between the degenerate vacua in curvedspace. We show that there exist $O(4)$-symmetric solutions not only in deSitter but also in both flat and anti-de Sitter space. The geometry of the newtype of solutions is finite and preserves the $Z_2$ symmetry. The nontrivialsolution corresponding to the tunneling is possible only if gravity is takeninto account. The numerical solutions as well as the analytic computationsusing the thin-wall approximation are presented. We expect that these solutionsdo not have any negative mode as in the instanton solution.

Instanton solutions mediating tunneling between the degenerate vacua in curved space