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

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