The Cauchy problem for the Klein-Gordon equation under the quartic potential in the de Sitter spacetime

TL;DR

This paper investigates the global existence of solutions to the Klein-Gordon equation with a quartic potential in de Sitter spacetime, highlighting the role of spontaneous symmetry breaking and spacetime expansion or contraction.

Contribution

It demonstrates the existence of global solutions considering the effects of spacetime dynamics and spontaneous symmetry breaking in a specific quantum field model.

Findings

Global solutions exist for small positive Hubble constant.

Spacetime expansion and contraction influence solution behavior.

Spontaneous symmetry breaking facilitates solution existence.

Abstract

The Cauchy problem for the Klein-Gordon equation under the quartic potential is considered in the de Sitter spacetime. The existence of the global solution is shown based on the mechanism of the spontaneous symmetry breaking for the small positive Hubble constant. The effects of the spatial expansion and contraction on the problem are considered.