Oscillating instanton solutions in curved space

Details Oscillating instanton solutions in curved space Oscillating instanton solutions in curved space

2011-06-29

arxiv.org/abs/1106.5865v2

Phys.Rev.D85:024022,2012

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, 11 figues. Some typos corrected, references added, and Ch3. modified according to referee's comments

Scientific paper

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.

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