Global solutions to the spherically symmetric Einstein-scalar field system with a positive cosmological constant in Bondi coordinates

Abstract

We consider a characteristic initial value problem, with initial data given on a future null cone, for the Einstein (massless) scalar field system with a positive cosmological constant, in Bondi coordinates. We prove that, for small data, this system has a unique global classical solution which is causally geodesically complete to the future and decays polynomially in radius and exponentially in Bondi time, approaching the de Sitter solution.

25 pages, to appear in Journal of Hyperbolic Differential Equations