7 research outputs found
Late-time behaviour of the tilted Bianchi type VI models
We study tilted perfect fluid cosmological models with a constant equation of
state parameter in spatially homogeneous models of Bianchi type VI
using dynamical systems methods and numerical simulations. We study models with
and without vorticity, with an emphasis on their future asymptotic evolution.
We show that for models with vorticity there exists, in a small region of
parameter space, a closed curve acting as the attractor.Comment: 13 pages, 1 figure, v2: typos fixed, minor changes, matches published
versio
The Futures of Bianchi type VII0 cosmologies with vorticity
We use expansion-normalised variables to investigate the Bianchi type VII
model with a tilted -law perfect fluid. We emphasize the late-time
asymptotic dynamical behaviour of the models and determine their asymptotic
states. Unlike the other Bianchi models of solvable type, the type VII
state space is unbounded. Consequently we show that, for a general
non-inflationary perfect fluid, one of the curvature variables diverges at late
times, which implies that the type VII model is not asymptotically
self-similar to the future. Regarding the tilt velocity, we show that for
fluids with (which includes the important case of dust,
) the tilt velocity tends to zero at late times, while for a
radiation fluid, , the fluid is tilted and its vorticity is
dynamically significant at late times. For fluids stiffer than radiation
(), the future asymptotic state is an extremely tilted spacetime
with vorticity.Comment: 23 pages, v2:references and comments added, typos fixed, to appear in
CQ
A geometric description of the intermediate behaviour for spatially homogeneous models
A new approach is suggested for the study of geometric symmetries in general
relativity, leading to an invariant characterization of the evolutionary
behaviour for a class of Spatially Homogeneous (SH) vacuum and orthogonal
law perfect fluid models. Exploiting the 1+3 orthonormal frame
formalism, we express the kinematical quantities of a generic symmetry using
expansion-normalized variables. In this way, a specific symmetry assumption
lead to geometric constraints that are combined with the associated
integrability conditions, coming from the existence of the symmetry and the
induced expansion-normalized form of the Einstein's Field Equations (EFE), to
give a close set of compatibility equations. By specializing to the case of a
\emph{Kinematic Conformal Symmetry} (KCS), which is regarded as the direct
generalization of the concept of self-similarity, we give the complete set of
consistency equations for the whole SH dynamical state space. An interesting
aspect of the analysis of the consistency equations is that, \emph{at least}
for class A models which are Locally Rotationally Symmetric or lying within the
invariant subset satisfying , a proper KCS \emph{always
exists} and reduces to a self-similarity of the first or second kind at the
asymptotic regimes, providing a way for the ``geometrization'' of the
intermediate epoch of SH models.Comment: Latex, 15 pages, no figures (uses iopart style/class files); added
one reference and minor corrections; (v3) improved and extended discussion;
minor corrections and several new references are added; to appear in Class.
Quantum Gra