Instanton solutions mediating tunneling between the degenerate vacua in curved space

Understand

We investigate the instanton solution between the degenerate vacua in curved space.

• We show that there exist $O(4)$-symmetric solutions not only in de Sitter but also in both flat and anti-de Sitter space.
• The geometry of the new type of solutions is finite and preserves the $Z_2$ symmetry.
• The nontrivial solution corresponding to the tunneling is possible only if gravity is taken into account.