On the Cosmic NoHair Conjecture in T2symmetric nonlinear scalar field spacetimes
Abstract
We consider spacetimes solving the Einstein nonlinear scalar field equations with T2symmetry and show that they admit an areal time foliation in the expanding direction. In particular, we prove global existence and uniqueness of solutions to the corresponding system of evolution equations for all future times. The only assumption we have to make is that the potential is a nonnegative smooth function. In the special case of a constant potential, a setting which is equivalent to a linear scalar field on a background with a positive cosmological constant, we achieve detailed asymptotic estimates for the different components of the spacetime metric. This result holds for all T3Gowdy symmetric metrics and extends to certain T2symmetric ones satisfying an a priori decay property. Building upon these asymptotic estimates, we show future causal geodesic completeness and prove the Cosmic NoHair conjecture.
 Publication:

arXiv eprints
 Pub Date:
 December 2017
 DOI:
 10.48550/arXiv.1712.01801
 arXiv:
 arXiv:1712.01801
 Bibcode:
 2017arXiv171201801R
 Keywords:

 General Relativity and Quantum Cosmology;
 Mathematical Physics;
 Mathematics  Differential Geometry
 EPrint:
 32 pages