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In many cases a massive nonlinear scalar field can lead to acceleratedexpansion in cosmological models. This paper contains mathematical results onthis subject for flat Robertson-Walker space-time. Global existence to thecoupled Einstein-massive scalar field system which rules the dynamics of a kindof pure matter in the presence of a massive scalar field and cosmologicalconstant is proved, under the assumption that the scalar field ? is anon-decreasing function, in Robertson-Walker1 space-time; asymptotic behaviourare investigated in the case of a cosmological constant bounded from below by astrictly negative constant depending only on the massive scalar field.

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