Fubini instantons in curved space

TL;DR

This paper investigates Fubini instantons in curved spacetime, revealing new solutions influenced by gravity, including Z2 symmetric solutions in de Sitter space, expanding understanding of vacuum decay mechanisms.

Contribution

It introduces novel O(4)-symmetric Fubini instanton solutions in curved space, highlighting gravity's role and the existence of Z2 symmetric solutions in de Sitter backgrounds.

Findings

Multiple new instanton solutions found due to gravity effects

Z2 symmetric solutions exist only in de Sitter space

Gravity influences the tunneling process and solution structure

Abstract

We study Fubini instantons of a self-gravitating scalar field. The Fubini instanton describes the decay of a vacuum state under tunneling instead of rolling in the presence of a tachyonic potential. The tunneling occurs from the maximum of the potential, which is a vacuum state, to any arbitrary state, belonging to the tunneling without any barrier. We consider two different types of the tachyonic potential. One has only a quartic term. The other has both the quartic and quadratic terms. We show that, there exist several kinds of new O(4)-symmetric Fubini instanton solution, which are possible only if gravity is taken into account. One type of them has the structure with $Z_2$ symmetry. This type of the solution is possible only in the de Sitter background. We discuss on the interpretation of the solutions with $Z_2$ symmetry.