Global existence of the self-interacting scalar field in the de Sitter universe

Abstract

We present some sufficient conditions for the global in time existence of solutions of the semilinear Klein-Gordon equation of the self-interacting scalar field with complex mass. The coefficients of the equation depend on spatial variables as well, that makes results applicable, in particular, to the spacetime with the time slices being Riemannian manifolds. The least lifespan estimate is given for the class of equations including the Higgs boson equation, which according to physics has a finite lifetime.

References in corpus (6)

• Limits on the Higgs boson lifetime and width from its decay to four charged leptons
• Fundamental Solutions for the Klein-Gordon Equation in de Sitter Spacetime
• "Massless" vector field in de Sitter Universe
• de Sitter tachyons and related topics
• On Gravitational Waves in Spacetimes with a Nonvanishing Cosmological Constant
• Waves in the Witten Bubble of Nothing and the Hawking Wormhole

Cited by in corpus (6)

• The Cauchy problem for the Klein-Gordon equation under the quartic potential in the de Sitter spacetime
• A note on blow-up results for semilinear wave equations in de Sitter and anti-de Sitter spacetimes
• The global existence of small self-interacting scalar field propagating in the contracting universe
• Waves in cosmological background with static Schwarzschild radius in the expanding universe
• On a semilinear wave equation in anti-de Sitter spacetime: the critical case
• Semilinear wave equations on accelerated expanding FLRW spacetimes