Blowup of the solution to the Cauchy problem with arbitrary positive energy for a system of Klein–Gordon equations in the de Sitter metric

Abstract

The ϕ⁴ model of a scalar (complex) field in the metric of an expanding universe, namely, in the de Sitter metric is considered. The initial energy of the system can have an arbitrarily high positive value. Sufficient conditions for solution blowup in a finite time are obtained. The existence of blowup is proved by applying H.A. Levine’s modified method is used.