Small solutions of the Einstein-Boltzmann-scalar field system with Bianchi symmetry

Abstract

We show that small homogeneous solutions to the Einstein-Boltzmann-scalar field system exist globally towards the future and tend to the de Sitter solution in a suitable sense. More specifically, we assume that the spacetime is of Bianchi type I--VIII, that the matter is described by Israel particles and that there exists a scalar field with a potential which has a positive lower bound. This represents a generalization of the work [19], where a cosmological constant was considered, and a generalization of [16], where a spatially flat FLRW spacetime was considered. We obtain the global existence and asymptotic behavior of classical solutions to the Einstein-Boltzmann-scalar field system for small initial data.

42 pages

References in corpus (1)

• Late-time behaviour of the Einstein-Boltzmann system with a positive cosmological constant

Cited by in corpus (2)

• Well-posedness of anisotropic and homogeneous solutions to the Einstein-Boltzmann system with a conformal-gauge singularity
• Future global existence of homogeneous solutions to the Einstein-Boltzmann system with soft potentials