27 research outputs found
Bianchi type IX asymptotical behaviours with a massive scalar field: chaos strikes back
We use numerical integrations to study the asymptotical behaviour of a
homogeneous but anisotropic Bianchi type IX model in General Relativity with a
massive scalar field. As it is well known, for a Brans-Dicke theory, the
asymptotical behaviour of the metric functions is ruled only by the Brans-Dicke
coupling constant with respect to the value -3/2. In this paper we examine if
such a condition still exists with a massive scalar field. We also show that,
contrary to what occurs for a massless scalar field, the singularity
oscillatory approach may exist in presence of a massive scalar field having a
positive energy density.Comment: 31 pages, 7 figures (low resolution
The Similarity Hypothesis in General Relativity
Self-similar models are important in general relativity and other fundamental
theories. In this paper we shall discuss the ``similarity hypothesis'', which
asserts that under a variety of physical circumstances solutions of these
theories will naturally evolve to a self-similar form. We will find there is
good evidence for this in the context of both spatially homogenous and
inhomogeneous cosmological models, although in some cases the self-similar
model is only an intermediate attractor. There are also a wide variety of
situations, including critical pheneomena, in which spherically symmetric
models tend towards self-similarity. However, this does not happen in all cases
and it is it is important to understand the prerequisites for the conjecture.Comment: to be submitted to Gen. Rel. Gra
Conditions for spontaneous homogenization of the Universe
The present-day Universe appears to be homogeneous on very large scales. Yet
when the casual structure of the early Universe is considered, it becomes
apparent that the early Universe must have been highly inhomogeneous. The
current paradigm attempts to answer this problem by postulating the inflation
mechanism However, inflation in order to start requires a homogeneous patch of
at least the horizon size. This paper examines if dynamical processes of the
early Universe could lead to homogenization. In the past similar studies seem
to imply that the set of initial conditions that leads to homogenization is of
measure zero. This essay proves contrary: a set of initial conditions for
spontaneous homogenization of cosmological models can form a set of non-zero
measure.Comment: 7 pages. Fifth Award in the 2010 Gravity Research Foundation essay
competitio
Bianchi Type V Viscous Fluid Cosmological Models in Presence of Decaying Vacuum Energy
Bianchi type V viscous fluid cosmological model for barotropic fluid
distribution with varying cosmological term is investigated. We have
examined a cosmological scenario proposing a variation law for Hubble parameter
in the background of homogeneous, anisotropic Bianchi type V space-time.
The model isotropizes asymptotically and the presence of shear viscosity
accelerates the isotropization. The model describes a unified expansion history
of the universe indicating initial decelerating expansion and late time
accelerating phase. Cosmological consequences of the model are also discussed.Comment: 10 pages, 3 figure
Dynamics of a self-gravitating neutron source
We examine the dynamics of a self--gravitating magnetized neutron gas as a
source of a Bianchi I spacetime described by the Kasner metric. The set of
Einstein-Maxwell field equations can be expressed as a dynamical system in a
4-dimensional phase space. Numerical solutions of this system reveal the
emergence of a point--like singularity as the final evolution state for a large
class of physically motivated initial conditions. Besides the theoretical
interest of studying this source in a fully general relativistic context, the
resulting idealized model could be helpful in understanding the collapse of
local volume elements of a neutron gas in the critical conditions that would
prevail in the center of a compact object.Comment: 17 pages, 6 figures, JHEP style, published versio
Light propagation in statistically homogeneous and isotropic universes with general matter content
We derive the relationship of the redshift and the angular diameter distance
to the average expansion rate for universes which are statistically homogeneous
and isotropic and where the distribution evolves slowly, but which have
otherwise arbitrary geometry and matter content. The relevant average expansion
rate is selected by the observable redshift and the assumed symmetry properties
of the spacetime. We show why light deflection and shear remain small. We write
down the evolution equations for the average expansion rate and discuss the
validity of the dust approximation.Comment: 42 pages, no figures. v2: Corrected one detail about the angular
diameter distance and two typos. No change in result