Future global existence of homogeneous solutions to the Einstein-Boltzmann system with soft potentials

Fuente: arXiv
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Main Authors: Lee, Ho, Nungesser, Ernesto
Format: Preprint
Published: 2023
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author Lee, Ho
Nungesser, Ernesto
author_facet Lee, Ho
Nungesser, Ernesto
contents We study the Cauchy problem for the Einstein-Boltzmann system with soft potentials in a cosmological setting. We assume the Bianchi I symmetry to describe a spatially homogeneous, but anisotropic universe and consider a cosmological constant $ Λ> 0 $ to describe an accelerated expansion of the universe. For the Boltzmann equation we introduce a new weight function and apply the method of Illner and Shinbrot to obtain the future global existence of spatially homogeneous, small solutions. For the Einstein equations we assume that the initial value of the Hubble variable is close to $ ( Λ/ 3 )^{ 1 / 2 } $. We obtain the future global existence and asymptotic behavior of spatially homogeneous solutions to the Einstein-Boltzmann system with soft potentials.
format Preprint
id arxiv_https___arxiv_org_abs_2311_03209
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Future global existence of homogeneous solutions to the Einstein-Boltzmann system with soft potentials
Lee, Ho
Nungesser, Ernesto
General Relativity and Quantum Cosmology
Mathematical Physics
We study the Cauchy problem for the Einstein-Boltzmann system with soft potentials in a cosmological setting. We assume the Bianchi I symmetry to describe a spatially homogeneous, but anisotropic universe and consider a cosmological constant $ Λ> 0 $ to describe an accelerated expansion of the universe. For the Boltzmann equation we introduce a new weight function and apply the method of Illner and Shinbrot to obtain the future global existence of spatially homogeneous, small solutions. For the Einstein equations we assume that the initial value of the Hubble variable is close to $ ( Λ/ 3 )^{ 1 / 2 } $. We obtain the future global existence and asymptotic behavior of spatially homogeneous solutions to the Einstein-Boltzmann system with soft potentials.
title Future global existence of homogeneous solutions to the Einstein-Boltzmann system with soft potentials
topic General Relativity and Quantum Cosmology
Mathematical Physics
url https://arxiv.org/abs/2311.03209