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–Lamaître–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.

中文翻译：

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在收缩宇宙中传播的自相互作用小标量场的整体存在

我们提出了一个关于自相互作用项的条件，该条件保证了紧缩宇宙的弗里德曼-拉马特-罗伯逊-沃克模型中半线性Klein-Gordon方程的柯西问题的整体时间解的存在。对于具有希格斯势能的Klein-Gordon方程，我们给出了溶液寿命的较低估计。