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

Abstract

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.

23 pages, 2 figures; v2: minor changes, references added, matches final published version

References in corpus (2)

• Non-genericity of the Nariai solutions: I. Asymptotics and spatially homogeneous perturbations
• Non-genericity of the Nariai solutions: II. Investigations within the Gowdy class

Cited by in corpus (2)

• Future dynamics of FLRW for the massless-scalar field system with positive cosmological constant
• Cosmic no-hair in spherically symmetric black hole spacetimes