4 research outputs found
Intermediate inflation and the slow-roll approximation
It is shown that spatially homogeneous solutions of the Einstein equations
coupled to a nonlinear scalar field and other matter exhibit accelerated
expansion at late times for a wide variety of potentials . These potentials
are strictly positive but tend to zero at infinity. They satisfy restrictions
on and related to the slow-roll approximation. These results
generalize Wald's theorem for spacetimes with positive cosmological constant to
those with accelerated expansion driven by potentials belonging to a large
class.Comment: 19 pages, results unchanged, additional backgroun
Accelerated cosmological expansion due to a scalar field whose potential has a positive lower bound
In many cases a nonlinear scalar field with potential can lead to
accelerated expansion in cosmological models. This paper contains mathematical
results on this subject for homogeneous spacetimes. It is shown that, under the
assumption that has a strictly positive minimum, Wald's theorem on
spacetimes with positive cosmological constant can be generalized to a wide
class of potentials. In some cases detailed information on late-time
asymptotics is obtained. Results on the behaviour in the past time direction
are also presented.Comment: 16 page
The Einstein-Vlasov System/Kinetic Theory
The main purpose of this article is to provide a guide to theorems on global
properties of solutions to the Einstein--Vlasov system. This system couples
Einstein's equations to a kinetic matter model. Kinetic theory has been an
important field of research during several decades in which the main focus has
been on non-relativistic and special relativistic physics, i.e., to model the
dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In
1990, Rendall and Rein initiated a mathematical study of the Einstein--Vlasov
system. Since then many theorems on global properties of solutions to this
system have been established.Comment: Published version http://www.livingreviews.org/lrr-2011-