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

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.

References in corpus (9)

• Fine Structure of Oscillons in the Spherically Symmetric ${\varphi }^4$ Klein-Gordon Model
• de Sitter tachyons and related topics
• Semilinear wave equations on asymptotically de Sitter, Kerr-de Sitter and Minkowski spacetimes
• Wobbling kinks in ${\varphi }^4$ theory
• Global existence of the self-interacting scalar field in the de Sitter universe
• A Strichartz estimate for de Sitter space
• Spontaneous symmetry breaking and Higgs mode: comparing Gross-Pitaevskii and nonlinear Klein-Gordon equations
• On the numerical experiments of the Cauchy problem for semi-linear Klein-Gordon equations in the de Sitter spacetime
• The global existence of small self-interacting scalar field propagating in the contracting universe

Cited by in corpus (3)

• A note on blow-up results for semilinear wave equations in de Sitter and anti-de Sitter spacetimes
• On a semilinear wave equation in anti-de Sitter spacetime: the critical case
• Numerical accuracy and stability of semilinear Klein--Gordon equation in de Sitter spacetime