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Global in time existence of self-interacting scalar field in de Sitter spacetimes. (English) Zbl 1352.83005

Summary: We prove the existence of a global in time solution of the semilinear Klein-Gordon equation in the de Sitter space-time. The coefficients of the equation depend on spatial variables as well, that make results applicable to the space-time with the time slices being Riemannian manifolds.

MSC:

83C15 Exact solutions to problems in general relativity and gravitational theory
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
53Z05 Applications of differential geometry to physics
53C12 Foliations (differential geometric aspects)
35Q75 PDEs in connection with relativity and gravitational theory
35L05 Wave equation
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References:

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