Oscillating instanton solutions in curved space

TL;DR

This paper explores oscillating instanton solutions in curved spacetime with gravity, revealing their properties, existence conditions, and potential implications for domain walls and topological inflation.

Contribution

It demonstrates the existence of O(4)-symmetric oscillating instantons in de Sitter space, including their phase diagram and physical interpretation as thick wall nucleation mechanisms.

Findings

Existence of finite, Z2-symmetric oscillating solutions in de Sitter space.

Solutions can be interpreted as instanton-induced thick walls for inflation.

Presence of solutions in flat and anti-de Sitter backgrounds, with unclear physical significance.

Abstract

We investigate oscillating instanton solutions of a self-gravitating scalar field between degenerate vacua. We show that there exist O(4)-symmetric oscillating solutions in a de Sitter background. The geometry of this solution is finite and preserves the $Z_{2}$ symmetry. The nontrivial solution corresponding to tunneling is possible only if the effect of gravity is taken into account. We present numerical solutions of this instanton, including the phase diagram of solutions in terms of the parameters of the present work and the variation of energy densities. Our solutions can be interpreted as solutions describing an instanton-induced domain wall or braneworld-like object rather than a kink-induced domain wall or braneworld. The oscillating instanton solutions have a thick wall and the solutions can be interpreted as a mechanism providing nucleation of the thick wall for topological inflation. We remark that $Z_{2}$ invariant solutions also exist in a flat and anti-de Sitter background, though the physical significance is not clear.