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

## TL;DR

This paper establishes conditions ensuring the global existence of solutions for a self-interacting scalar field equation in de Sitter universe, with applications to physically relevant models like the Higgs boson.

## Contribution

It provides new sufficient conditions for global solutions of a semilinear Klein-Gordon equation with spatially dependent coefficients, extending applicability to curved spacetimes.

## Key findings

- Conditions for global existence of solutions
- Lifespan estimates for Higgs-like equations
- Applicability to spacetime with Riemannian slices

## 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.