Power Law Inflation
2009 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 290, no 1, 155-218 p.Article in journal (Refereed) Published
The subject of this paper is Einstein's equations coupled to a non-linear scalar field with an exponential potential. The problem we consider is that of proving future global non-linear stability of a class of spatially locally homogeneous solutions to the equations. There are solutions on R(+)xR(n) with accelerated expansion of power law type. We prove a result stating that if we have initial data that are close enough to those of such a solution on a ball of a certain radius, say B-4R0 (p), then all causal geodesics starting in B-R0 (p) are complete to the future in the maximal globally hyperbolic development of the data we started with. In other words, we only make local assumptions in space and obtain global conclusions in time. We also obtain asymptotic expansions in the region over which we have control. As a consequence of this result and the fact that one can analyze the asymptotic behaviour in most of the spatially homogeneous cases, we obtain quite a general stability statement in the spatially locally homogeneous setting.
Place, publisher, year, edition, pages
2009. Vol. 290, no 1, 155-218 p.
scalar field system, equations, existence, spacetimes, manifolds, stability
IdentifiersURN: urn:nbn:se:kth:diva-18548DOI: 10.1007/s00220-009-0812-6ISI: 000267391700007ScopusID: 2-s2.0-70349684754OAI: oai:DiVA.org:kth-18548DiVA: diva2:336595
QC 201005252010-08-052010-08-052012-04-14Bibliographically approved