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arXiv · 1206.4153

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

Joao L. Costa·Artur Alho·Jose Natario
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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.

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Joao L. Costa, Artur Alho, Jose Natario. 2012-06-19. The problem of a self-gravitating scalar field with positive cosmological constant. https://doi.org/10.1007/s00023-012-0215-7

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