The problem of a self-gravitating scalar field with positive cosmological constant

• Autor(a) principal: Costa, J. L.
• Data de Publicação: 2013
• Outros Autores: Alho, A., Natário, J.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: https://ciencia.iscte-iul.pt/public/pub/id/12697; http://hdl.handle.net/10071/11800

We study the Einstein-scalar field system with positive cosmological constant and spherically symmetric characteristic initial data given on a truncated null cone. We prove well-posedness, global existence and exponential decay in (Bondi) time, for small data. From this, it follows that initial data close enough to de Sitter data evolves to a causally geodesically complete spacetime (with boundary), which approaches a region of de Sitter asymptotically at an exponential rate; this is a non-linear stability result for de Sitter within the class under consideration, as well as a realization of the cosmic no-hair conjecture.