Instanton solutions mediating tunneling between the degenerate vacua in curved space

TL;DR

This paper explores instanton solutions that enable tunneling between degenerate vacua in various curved spacetimes, revealing new symmetric solutions influenced by gravity, with potential implications for quantum field theory in curved backgrounds.

Contribution

It demonstrates the existence of $O(4)$-symmetric instanton solutions in flat, de Sitter, and anti-de Sitter spaces, highlighting gravity's role in enabling these tunneling phenomena.

Findings

Existence of $O(4)$-symmetric solutions in multiple curved spacetimes.

Finite geometry of solutions preserving $Z_2$ symmetry.

Solutions likely free of negative modes, indicating stability.

Abstract

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. The numerical solutions as well as the analytic computations using the thin-wall approximation are presented. We expect that these solutions do not have any negative mode as in the instanton solution.