The global existence of small self-interacting scalar field propagating in the contracting universe

TL;DR

This paper establishes conditions ensuring global solutions for a self-interacting scalar field in a contracting universe, providing lifespan estimates for specific potentials like the Higgs potential.

Contribution

It introduces a new condition on the self-interaction term that guarantees global existence of solutions in a contracting universe setting.

Findings

Derived a condition for global existence of solutions.

Provided lifespan estimates for solutions with Higgs potential.

Analyzed the Klein-Gordon equation in a cosmological model.

Abstract

We present a condition on the self-interaction term that guaranties the existence of the global in time solution of the Cauchy problem for the semilinear Klein-Gordon equation in the Friedmann-Lama$\hat{i}$tre-Robertson-Walker model of the contracting universe. For the Klein-Gordon equation with the Higgs potential we give a lower estimate for the lifespan of solution.