Global existence of solutions to the Einstein-massive scalar field equations with a cosmological constant for a perfect fluid on the flat Robertson-Walker space-time

TL;DR

This paper proves the global existence of solutions to the Einstein-massive scalar field equations with a cosmological constant in flat Robertson-Walker space-time, analyzing their asymptotic behavior under specific conditions.

Contribution

It provides the first rigorous proof of global solutions for this coupled system with a non-decreasing scalar field and investigates their long-term behavior.

Findings

Global existence of solutions established

Asymptotic behavior characterized for negative cosmological constants

Conditions on scalar field growth are identified

Abstract

In many cases a massive nonlinear scalar field can lead to accelerated expansion in cosmological models. This paper contains mathematical results on this subject for flat Robertson-Walker space-time. Global existence to the coupled Einstein-massive scalar field system which rules the dynamics of a kind of pure matter in the presence of a massive scalar field and cosmological constant is proved, under the assumption that the scalar field ? is a non-decreasing function, in Robertson-Walker1 space-time; asymptotic behaviour are investigated in the case of a cosmological constant bounded from below by a strictly negative constant depending only on the massive scalar field.